Exploring Treatment x Trial Interactions using Treatment Stability/Trial Dendrogram plots
Peter Claussen
October 15, 2015
lambda <- c(0.04,-0.191,0.028,0.037,-0.021,0.085,0.015,-0.135,-0.004,0.021,-0.011,0.018,0.022,-0.1,0.047)
year <- as.factor(c(2007,2007,2007,2003,2003,2003,2004,2004,2004,2005,2005,2005,2006,2006,2006))
variable <-as.factor(c("GY","TW","HD","GY","TW","HD","GY","TW","HD","GY","TW","HD","GY","TW","HD"))
tapply(lambda,list(variable),mean)## GY HD TW
## 0.0270 0.0348 -0.0916tapply(lambda,list(variable),sd)## GY HD TW
## 0.01088577 0.03355145 0.07634658Here I use the CPT 2007 data set to illustrate new options avialable for ST Treatment Stability/Trial Dendrogram plots.
Multilocation
Using scripts from ARM ST to show options.
cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbbPalette <- c("#000000", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbColors <- c(cbPalette,cbbPalette)
path = "../Manuscripts/scripts/multilocation"
means.vector <- read.delim('../Manuscripts/scripts/multilocation/trialMeans.SmyCol1.tab',header=FALSE)
means.matrix <- read.delim('../Manuscripts/scripts/multilocation/trialTable.SmyCol1.tab',header=FALSE)
means.vector <- means.vector[,1]
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 6, 2, 1) + 0.1), ps = 12, cex.lab = 1.166667, cex.main = 1.333333, cex.axis = 1)
res1<-plot.interaction.ARMST(means.matrix, means.vector, ylab='Treatment in Trial Mean \nYield',regression=TRUE, main='Treatment Stability and Trial Clusters for Grand Mean 1', show.legend=TRUE,legend.columns=1, legend.pos=c(.01,.98),trt.colors=cbColors)
par(fig=c(0,1,0,.4),mar=(c(4, 6, 0, 1) + 0.1), new=TRUE)
res2<-plot.clusters.ARMST(means.matrix, means.vector, xlab='Trial Mean \nMultilocation', ylab='',trt.colors =cbColors)
par(fig = c(0, 1, 0, 1))path = "../Manuscripts/scripts/multilocation"
means.vector <- read.delim('../Manuscripts/scripts/multilocation/trialMeans.SmyCol1.tab',header=FALSE)
means.matrix <- read.delim('../Manuscripts/scripts/multilocation/trialTable.SmyCol1.tab',header=FALSE)
means.vector <- means.vector[,1]
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 6, 2, 1) + 0.1), ps = 12, cex.lab = 1.166667, cex.main = 1.333333, cex.axis = 1)
res1<-plot.interaction.ARMST(means.matrix, means.vector, ylab='Treatment in Trial Mean \nYield',regression=TRUE, main='Treatment Stability and Trial Clusters for Grand Mean 1', show.legend=TRUE,legend.columns=1, legend.pos=c(.01,.98),trt.colors=cbColors)
par(fig=c(0,1,0,.4),mar=(c(4, 6, 0, 1) + 0.1), new=TRUE)
decomp <- decompose.means.table(means.matrix)
fg="black"
res2<-plot.clusters.ARMST(means.matrix, means.vector, fg=fg,xlab='Trial Mean \nMultilocation', ylab='',reference=(decomp$mu + decomp$alpha + decomp$beta),trt.colors=cbColors)
fg=cbColors[2]
res3 <- plot.clusters.ARMST(decomp$mu + decomp$alpha + decomp$beta, means.vector, fg=fg,add=TRUE,xlab='Trial Mean \nMultilocation', ylab='',trt.colors=cbColors)
par(fig = c(0, 1, 0, 1))str(res2$means.hc)## List of 7
## $ merge : int [1:8, 1:2] -6 -1 -5 -4 2 -2 1 6 -8 -3 ...
## $ height : num [1:8] 0.168 0.227 0.385 0.423 0.507 ...
## $ order : int [1:9] 2 4 9 6 8 1 3 5 7
## $ labels : NULL
## $ method : chr "complete"
## $ call : language hclust(d = dist(means.matrix), method = method)
## $ dist.method: chr "euclidean"
## - attr(*, "class")= chr "hclust"res2$means.hc$height## [1] 0.1680609 0.2272786 0.3849098 0.4228869 0.5068531 0.5913357 0.9790983
## [8] 1.9802638res3$means.hc$height## [1] 0.05000015 0.05500003 0.10166665 0.12000000 0.42166670 0.44333339
## [7] 0.96833340 1.94666672res2$means.hc$height/res3$means.hc$height## [1] 3.361208 4.132335 3.785999 3.524058 1.202023 1.333840 1.011117 1.017259res2$means.hc$order## [1] 2 4 9 6 8 1 3 5 7res3$means.hc$order## [1] 2 4 9 6 8 5 7 1 3res2$means.hc$merge## [,1] [,2]
## [1,] -6 -8
## [2,] -1 -3
## [3,] -5 -7
## [4,] -4 -9
## [5,] 2 3
## [6,] -2 4
## [7,] 1 5
## [8,] 6 7res3$means.hc$merge## [,1] [,2]
## [1,] -5 -7
## [2,] -4 -9
## [3,] -1 -3
## [4,] -6 -8
## [5,] 1 3
## [6,] -2 2
## [7,] 4 5
## [8,] 6 7res2$means.hc$merge==res3$means.hc$merge## [,1] [,2]
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,] FALSE FALSE
## [5,] FALSE TRUE
## [6,] TRUE FALSE
## [7,] FALSE TRUE
## [8,] TRUE TRUEmatched.idx <- compare.merges(res2$means.hc$merge,res3$means.hc$merge)
matched.idx## [1] 4 3 1 2 0 0 0 8res2$means.hc$height## [1] 0.1680609 0.2272786 0.3849098 0.4228869 0.5068531 0.5913357 0.9790983
## [8] 1.9802638res3$means.hc$height## [1] 0.05000015 0.05500003 0.10166665 0.12000000 0.42166670 0.44333339
## [7] 0.96833340 1.94666672res3$means.hc$height[matched.idx]## [1] 0.12000000 0.10166665 0.05000015 0.05500003 1.94666672The function cluster.stats() in the fpc package provides a mechanism for comparing the similarity of two cluster solutions using a variety of validation criteria (Hubert’s gamma coefficient, the Dunn index and the corrected rand index) # comparing 2 cluster solutions
library(fpc)
d <- dist(means.matrix)
cluster.stats(d, res2$clusters, res3$clusters)## $n
## [1] 9
##
## $cluster.number
## [1] 3
##
## $cluster.size
## [1] 4 3 2
##
## $min.cluster.size
## [1] 2
##
## $noisen
## [1] 0
##
## $diameter
## [1] 0.5068531 0.5913357 0.1680609
##
## $average.distance
## [1] 0.4002332 0.5152329 0.1680609
##
## $median.distance
## [1] 0.4055768 0.5314759 0.1680609
##
## $separation
## [1] 0.5229192 0.5952870 0.5229192
##
## $average.toother
## [1] 0.8850877 1.1943831 1.1381486
##
## $separation.matrix
## [,1] [,2] [,3]
## [1,] 0.0000000 0.595287 0.5229192
## [2,] 0.5952870 0.000000 1.4083008
## [3,] 0.5229192 1.408301 0.0000000
##
## $ave.between.matrix
## [,1] [,2] [,3]
## [1,] 0.0000000 0.9694404 0.7585586
## [2,] 0.9694404 0.0000000 1.6442685
## [3,] 0.7585586 1.6442685 0.0000000
##
## $average.between
## [1] 1.060283
##
## $average.within
## [1] 0.4115159
##
## $n.between
## [1] 26
##
## $n.within
## [1] 10
##
## $max.diameter
## [1] 0.5913357
##
## $min.separation
## [1] 0.5229192
##
## $within.cluster.ss
## [1] 0.5365621
##
## $clus.avg.silwidths
## 1 2 3
## 0.4281916 0.4560306 0.7772011
##
## $avg.silwidth
## [1] 0.5150289
##
## $g2
## NULL
##
## $g3
## NULL
##
## $pearsongamma
## [1] 0.646884
##
## $dunn
## [1] 0.8843018
##
## $dunn2
## [1] 1.472264
##
## $entropy
## [1] 1.060857
##
## $wb.ratio
## [1] 0.3881188
##
## $ch
## [1] 18.8348
##
## $cwidegap
## [1] 0.3865230 0.5314759 0.1680609
##
## $widestgap
## [1] 0.5314759
##
## $sindex
## [1] 0.5229192
##
## $corrected.rand
## [1] 1
##
## $vi
## [1] 0where d is a distance matrix among objects, and fit1\(cluster and fit\)cluster are integer vectors containing classification results from two different clusterings of the same data.
library(SASmixed)
data(Multilocation)
mixed.res <- standard.sensitivity.plot(Multilocation,
response = "Adj",
TreatmentName = "Trt",
TrialName = "Location",
RepName="Block",
dual.dendrogram=TRUE,
plot.outliers=TRUE,legend.columns=1)## Loading required package: lme4## Loading required package: Matrix## Warning: package 'Matrix' was built under R version 3.3.2## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?
print.stdplot(mixed.res)## [1] ----------------------------------------------------
## [1] Effects
## [,1]
## 1 0.2822880
## 2 -0.6257370
## 3 0.2254713
## 4 -0.6476620
## 5 -0.1976037
## 6 0.2619546
## 7 0.3421963
## 8 0.5393880
## 9 -0.1802954
## [,1]
## 1 0.047525000
## 2 -0.086008333
## 3 0.029625000
## 4 0.008858333
## [1] Means
## [,1]
## 1 2.999675
## 2 2.338883
## 3 2.874392
## 4 2.266025
## 5 2.946042
## 6 3.208492
## 7 3.140733
## 8 3.529417
## 9 2.384083
## [,1]
## 1 2.924011
## 2 2.677644
## 3 2.949452
## 4 2.865667
## [1] Row Col Means
## [1] 2.999675 2.297058 3.048608 2.550508 2.846858 3.258583 2.842475 3.322483
## [9] 2.521492
## X1 X2 X3 X4
## 2.924011 2.677644 2.949452 2.865667
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
##
## Response: Adj
## Df Sum Sq Mean Sq F value Pr(>F)
## Location 8 11.4635 1.43294 41.4400 < 2.2e-16 ***
## Trt 3 1.2217 0.40725 11.7774 4.803e-06 ***
## Location:Trt 24 0.9966 0.04152 1.2008 0.28285
## Location:Block 18 1.0270 0.05706 1.6500 0.07994 .
## Residuals 54 1.8672 0.03458
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: Adj ~ Location + (1 | Location/Block) + (1 | Location:Trt)
## Data: plot.dat
##
## REML criterion at convergence: 2.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.6168 -0.6321 0.0162 0.5230 2.8392
##
## Random effects:
## Groups Name Variance Std.Dev.
## Location:Trt (Intercept) 0.015860 0.12594
## Block:Location (Intercept) 0.005619 0.07496
## Location (Intercept) 0.028356 0.16839
## Residual 0.034579 0.18595
## Number of obs: 108, groups:
## Location:Trt, 36; Block:Location, 27; Location, 9
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.99968 0.19255 15.579
## LocationB -0.70262 0.27231 -2.580
## LocationC 0.04893 0.27231 0.180
## LocationD -0.44917 0.27231 -1.649
## LocationE -0.15282 0.27231 -0.561
## LocationF 0.25891 0.27231 0.951
## LocationG -0.15720 0.27231 -0.577
## LocationH 0.32281 0.27231 1.185
## LocationI -0.47818 0.27231 -1.756
##
## Correlation of Fixed Effects:
## (Intr) LoctnB LoctnC LoctnD LoctnE LoctnF LoctnG LoctnH
## LocationB -0.707
## LocationC -0.707 0.500
## LocationD -0.707 0.500 0.500
## LocationE -0.707 0.500 0.500 0.500
## LocationF -0.707 0.500 0.500 0.500 0.500
## LocationG -0.707 0.500 0.500 0.500 0.500 0.500
## LocationH -0.707 0.500 0.500 0.500 0.500 0.500 0.500
## LocationI -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## convergence code: 0
## Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?
##
## [1]
## [1] Stability
## [1] ----------------------------------------------------
## Treatment Slope Intercept Mean SD b
## 1 1 1.0681951 -0.12482441 2.924011 0.3852070 0.068195097
## 2 2 0.9601752 -0.06288138 2.677644 0.3403034 -0.039824803
## 3 3 1.0084981 0.07100300 2.949452 0.3584278 0.008498139
## 4 4 0.9631316 0.11670279 2.865667 0.3556809 -0.036868433
## Pb bR2
## 1 0.5890136 0.043775237
## 2 0.6447955 0.032068736
## 3 0.9287174 0.001226858
## 4 0.7959259 0.010207069
## [1]
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39512 -0.12950 -0.02166 0.11928 0.57024
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.06949 0.06738 45.557 < 2e-16 ***
## Trt2 -0.24637 0.05501 -4.478 2.09e-05 ***
## Trt3 0.02544 0.05501 0.462 0.644817
## Trt4 -0.05834 0.05501 -1.061 0.291581
## LocationB -0.70262 0.08252 -8.515 2.45e-13 ***
## LocationC 0.04893 0.08252 0.593 0.554597
## LocationD -0.44917 0.08252 -5.443 4.08e-07 ***
## LocationE -0.15282 0.08252 -1.852 0.067149 .
## LocationF 0.25891 0.08252 3.138 0.002269 **
## LocationG -0.15720 0.08252 -1.905 0.059805 .
## LocationH 0.32281 0.08252 3.912 0.000172 ***
## LocationI -0.47818 0.08252 -5.795 8.87e-08 ***
## eTrt:eLocation 0.26914 0.56130 0.480 0.632683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2021 on 95 degrees of freedom
## Multiple R-squared: 0.7658, Adjusted R-squared: 0.7363
## F-statistic: 25.89 on 12 and 95 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Trt 3 1.222 0.4072 9.968 8.95e-06 ***
## Location 8 11.464 1.4329 35.072 < 2e-16 ***
## eTrt:eLocation 1 0.009 0.0094 0.230 0.633
## Residuals 95 3.881 0.0409
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1]
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39061 -0.13704 -0.02025 0.12026 0.58668
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.064129 0.069661 43.986 < 2e-16 ***
## Trt2 -0.246367 0.055511 -4.438 2.49e-05 ***
## Trt3 0.025441 0.055511 0.458 0.647807
## Trt4 -0.058344 0.055511 -1.051 0.295965
## LocationB -0.676712 0.110941 -6.100 2.41e-08 ***
## LocationC 0.047129 0.083423 0.565 0.573474
## LocationD -0.432607 0.095550 -4.528 1.77e-05 ***
## LocationE -0.147183 0.084780 -1.736 0.085866 .
## LocationF 0.249363 0.087540 2.849 0.005406 **
## LocationG -0.151404 0.084867 -1.784 0.077682 .
## LocationH 0.310907 0.089821 3.461 0.000814 ***
## LocationI -0.460553 0.097071 -4.745 7.53e-06 ***
## Trt1:eLocation 0.105064 0.170386 0.617 0.538992
## Trt2:eLocation -0.002956 0.170386 -0.017 0.986194
## Trt3:eLocation 0.045367 0.170386 0.266 0.790630
## Trt4:eLocation NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.204 on 93 degrees of freedom
## Multiple R-squared: 0.7666, Adjusted R-squared: 0.7315
## F-statistic: 21.82 on 14 and 93 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39061 -0.13704 -0.02025 0.12026 0.58668
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Trt1 2.92401 0.03785 77.245 < 2e-16 ***
## Trt2 2.67764 0.03785 70.737 < 2e-16 ***
## Trt3 2.94945 0.03785 77.917 < 2e-16 ***
## Trt4 2.86567 0.03785 75.704 < 2e-16 ***
## Trt1:eLocation 1.06820 0.11619 9.194 5.79e-15 ***
## Trt2:eLocation 0.96018 0.11619 8.264 6.13e-13 ***
## Trt3:eLocation 1.00850 0.11619 8.680 7.67e-14 ***
## Trt4:eLocation 0.96313 0.11619 8.289 5.40e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1967 on 100 degrees of freedom
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9953
## F-statistic: 2884 on 8 and 100 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Trt 4 881.0 220.26 5693.16 <2e-16 ***
## Trt:eLocation 4 11.5 2.87 74.22 <2e-16 ***
## Residuals 100 3.9 0.04
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## Trt 3 1.222 0.4072 9.790 1.13e-05 ***
## Location 8 11.464 1.4329 34.445 < 2e-16 ***
## Trt:eLocation 3 0.022 0.0073 0.176 0.912
## Residuals 93 3.869 0.0416
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
## Estimate Std. Error t value Pr(>|t|)
## Trt1:eLocation 1.0681951 0.1161878 0.58693838 0.2792839
## Trt2:eLocation 0.9601752 0.1161878 -0.34276226 0.3662484
## Trt3:eLocation 1.0084981 0.1161878 0.07314139 0.4709199
## Trt4:eLocation 0.9631316 0.1161878 -0.31731751 0.3758321
## [1]
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 0.5578604
## [1] Interaction sd Value:
## [1] 0.1201781
## [1] Error sd Value:
## [1] 0.1859535
## [1] Pairs:
## list()
## [1]
## [1]response = "Plot.Mean"
TreatmentName = "Criteria.Entry.No."
TrialName = "Expt.No."
RepName="Rep.No."
#yield.desc ="Yield"
#tw.desc="Test Weight"
#hd.desc="Heading"
#ht.desc="Test Weight"
#cpt.dat <- read.csv("CPT.full.subset.csv",header=TRUE)
#cpt.dat <- read.csv("CPT_2007Subsetb.csv",header=TRUE)
yield.desc ="GY"
tw.desc ="TW"
hd.desc="HD"
ht.desc="HT"
cpt.dat <- read.delim("CPT_2007Subset.txt",header=TRUE)
cpt.dat <- subset(cpt.dat,!is.na(cpt.dat$Plot.Mean))
cpt.dat$Expt.No. <- as.factor(cpt.dat$Expt.No.)
TrtNames <- as.character(cpt.dat$Criteria.Entry.No.)
TrtNames[cpt.dat$Criteria.Entry.No.<10] <- paste("0",TrtNames[cpt.dat$Criteria.Entry.No.<10],sep="")
cpt.dat$Criteria.Entry.No. <- as.factor(TrtNames)
cpt.dat$Rep.No. <- as.factor(cpt.dat$Rep.No.)
gy.dat <- subset(cpt.dat,cpt.dat$Description==yield.desc)
tw.dat <- subset(cpt.dat,cpt.dat$Description==tw.desc)
hd.dat <- subset(cpt.dat,cpt.dat$Description==hd.desc)
ht.dat <- subset(cpt.dat,cpt.dat$Description==ht.desc)
gy.dat$Expt.No. <- as.factor(as.character(gy.dat$Expt.No.))
tw.dat$Expt.No. <- as.factor(as.character(tw.dat$Expt.No.))
hd.dat$Expt.No. <- as.factor(as.character(hd.dat$Expt.No.))
ht.dat$Expt.No. <- as.factor(as.character(ht.dat$Expt.No.))gy.means <- gei.table.and.effects(gy.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName)
gy.means$trial.means## [,1]
## 1 53.67708
## 2 55.57483
## 3 57.78769
## 4 39.01086
## 5 39.54350
## 6 33.59267
## 7 63.30659
## 8 67.83786
## 9 62.65739
## 10 26.95339
## 11 41.62739
## 12 39.34495
## 13 45.65942colMeans(gy.means$means.table)## [1] 53.67708 45.76792 56.31240 52.48333 44.91626 34.96458 55.53854
## [8] 58.18740 54.31667 30.64583 47.12352 48.92969 43.71042gy.res <- standard.sensitivity.plot(gy.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
dual.dendrogram=FALSE,
plot.outliers=TRUE,legend.columns=3)
gy.res <- standard.sensitivity.plot(gy.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
outliers=2.4,
dual.dendrogram=TRUE,
plot.outliers=TRUE,legend.columns=3)
print.stdplot(gy.res)## [1] ----------------------------------------------------
## [1] Effects
## [,1]
## 1 -0.8440639
## 2 7.3767696
## 3 15.5864568
## 4 -2.4336466
## 5 -11.9428351
## 6 -20.7732310
## 7 10.5778115
## 8 25.2331226
## 9 15.6730204
## 10 -21.8628136
## 11 -6.7127742
## 12 -10.6329185
## 13 0.7551020
## [,1]
## 1 -6.1020835
## 2 -2.0020831
## 3 1.0479161
## 4 -2.3020833
## 5 -1.2270835
## 6 4.1979157
## 7 0.4479176
## 8 -1.7020839
## 9 -1.6770833
## 10 -1.4020828
## 11 3.6229178
## 12 7.0979163
## [1] Means
## [,1]
## 1 53.67708
## 2 55.57483
## 3 57.78769
## 4 39.01086
## 5 39.54350
## 6 33.59267
## 7 63.30659
## 8 67.83786
## 9 62.65739
## 10 26.95339
## 11 41.62739
## 12 39.34495
## 13 45.65942
## [,1]
## 1 50.43968
## 2 48.36837
## 3 45.21639
## 4 35.26434
## 5 54.32460
## 6 56.79177
## 7 46.15985
## 8 43.17224
## 9 47.68186
## 10 51.02470
## 11 49.67348
## 12 50.25838
## [1] Row Col Means
## [1] 53.67708 45.76792 56.31240 52.48333 44.91626 34.96458 55.53854
## [8] 58.18740 54.31667 30.64583 47.12352 48.92969 43.71042
## X1 X2 X3 X4 X5 X6 X7 X8
## 50.43968 48.36837 45.21639 35.26434 54.32460 56.79177 46.15985 43.17224
## X9 X10 X11 X12
## 47.68186 51.02470 49.67348 50.25838
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
##
## Response: Plot.Mean
## Df Sum Sq Mean Sq F value Pr(>F)
## Expt.No. 12 39698 3308.2 194.3594 < 2.2e-16 ***
## Criteria.Entry.No. 11 17509 1591.7 93.5136 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132 19964 151.2 8.8856 < 2.2e-16 ***
## Expt.No.:Rep.No. 39 3998 102.5 6.0232 < 2.2e-16 ***
## Residuals 429 7302 17.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## Plot.Mean ~ Expt.No. + (1 | Expt.No./Rep.No.) + (1 | Expt.No.:Criteria.Entry.No.)
## Data: plot.dat
##
## REML criterion at convergence: 3977.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.95766 -0.49670 -0.00515 0.49975 2.82744
##
## Random effects:
## Groups Name Variance Std.Dev.
## Expt.No.:Criteria.Entry.No. (Intercept) 61.256 7.827
## Rep.No.:Expt.No. (Intercept) 7.125 2.669
## Expt.No. (Intercept) 32.377 5.690
## Residual 17.021 4.126
## Number of obs: 624, groups:
## Expt.No.:Criteria.Entry.No., 156; Rep.No.:Expt.No., 52; Expt.No., 13
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 53.6771 6.2942 8.528
## Expt.No.CPT:2007:Brookings -7.9092 8.9014 -0.889
## Expt.No.CPT:2007:DLakesPea 2.6353 8.9014 0.296
## Expt.No.CPT:2007:Hayes -1.1937 8.9014 -0.134
## Expt.No.CPT:2007:Kennebec -8.7608 8.9014 -0.984
## Expt.No.CPT:2007:Martin -18.7125 8.9014 -2.102
## Expt.No.CPT:2007:Onida 1.8615 8.9014 0.209
## Expt.No.CPT:2007:Platte 4.5103 8.9014 0.507
## Expt.No.CPT:2007:Selby 0.6396 8.9014 0.072
## Expt.No.CPT:2007:Sturgis -23.0312 8.9014 -2.587
## Expt.No.CPT:2007:Wall -6.5536 8.9014 -0.736
## Expt.No.CPT:2007:Watertown -4.7474 8.9014 -0.533
## Expt.No.CPT:2007:Winner -9.9667 8.9014 -1.120##
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(summary(fit$lmer), correlation=TRUE) or
## vcov(summary(fit$lmer)) if you need it## [1]
## [1] Stability
## [1] ----------------------------------------------------
## Treatment Slope Intercept Mean SD b
## 1 1 1.4470667 -19.3059998 50.43968 13.881179 0.447066711
## 2 2 1.1321911 -6.2009466 48.36837 10.210409 0.132191105
## 3 3 0.6213510 15.2685346 45.21639 8.308268 -0.378649035
## 4 4 0.5836777 7.1322629 35.26434 9.429917 -0.416322288
## 5 5 1.2073912 -3.8692090 54.32460 12.212059 0.207391158
## 6 6 1.2629921 -4.0818885 56.79177 12.518736 0.262992078
## 7 7 0.9908940 -1.5992298 46.15985 9.914119 -0.009105978
## 8 8 0.7606544 6.5102431 43.17224 7.677330 -0.239345577
## 9 9 0.9801060 0.4427417 47.68186 8.695932 -0.019894018
## 10 10 1.0053054 2.5710136 51.02470 8.950710 0.005305443
## 11 11 0.9178223 5.4363092 49.67348 8.668054 -0.082177704
## 12 12 1.0905481 -2.3038313 50.25838 9.701141 0.090548106
## Pb bR2
## 1 0.1044094 0.2216659526
## 2 0.3810162 0.0703845599
## 3 0.1377338 0.1889368944
## 4 0.1841813 0.1543568700
## 5 0.4304031 0.0574180092
## 6 0.3124248 0.0924748910
## 7 0.9646718 0.0001866071
## 8 0.1593920 0.1715657615
## 9 0.8615537 0.0028891132
## 10 0.9647863 0.0001853985
## 11 0.5949401 0.0265318385
## 12 0.4892785 0.0444565619
## [1]
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.2691 -4.1971 0.0708 4.0414 22.2588
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.918792 1.382298 40.454 < 2e-16 ***
## Criteria.Entry.No.02 -2.071312 1.382298 -1.498 0.134542
## Criteria.Entry.No.03 -5.223290 1.382298 -3.779 0.000173 ***
## Criteria.Entry.No.04 -15.175336 1.382298 -10.978 < 2e-16 ***
## Criteria.Entry.No.05 3.884915 1.382298 2.810 0.005109 **
## Criteria.Entry.No.06 6.352087 1.382298 4.595 5.27e-06 ***
## Criteria.Entry.No.07 -4.279829 1.382298 -3.096 0.002052 **
## Criteria.Entry.No.08 -7.267437 1.382298 -5.258 2.03e-07 ***
## Criteria.Entry.No.09 -2.757819 1.382298 -1.995 0.046485 *
## Criteria.Entry.No.10 0.585016 1.382298 0.423 0.672287
## Criteria.Entry.No.11 -0.766198 1.382298 -0.554 0.579585
## Criteria.Entry.No.12 -0.181305 1.382298 -0.131 0.895691
## Expt.No.CPT:2007:Brookings -7.909166 1.438741 -5.497 5.71e-08 ***
## Expt.No.CPT:2007:DLakesPea 2.635312 1.438741 1.832 0.067496 .
## Expt.No.CPT:2007:Hayes -1.193750 1.438741 -0.830 0.407029
## Expt.No.CPT:2007:Kennebec -8.760820 1.438741 -6.089 2.03e-09 ***
## Expt.No.CPT:2007:Martin -18.712500 1.438741 -13.006 < 2e-16 ***
## Expt.No.CPT:2007:Onida 1.861458 1.438741 1.294 0.196230
## Expt.No.CPT:2007:Platte 4.510312 1.438741 3.135 0.001803 **
## Expt.No.CPT:2007:Selby 0.639583 1.438741 0.445 0.656810
## Expt.No.CPT:2007:Sturgis -23.031250 1.438741 -16.008 < 2e-16 ***
## Expt.No.CPT:2007:Wall -6.553567 1.438741 -4.555 6.35e-06 ***
## Expt.No.CPT:2007:Watertown -4.747396 1.438741 -3.300 0.001025 **
## Expt.No.CPT:2007:Winner -9.966667 1.438741 -6.927 1.11e-11 ***
## eCriteria.Entry.No.:eExpt.No. 0.036771 0.006678 5.506 5.45e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.048 on 599 degrees of freedom
## Multiple R-squared: 0.6636, Adjusted R-squared: 0.6502
## F-statistic: 49.24 on 24 and 599 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 17509 1592 32.04 < 2e-16 ***
## Expt.No. 12 39698 3308 66.59 < 2e-16 ***
## eCriteria.Entry.No.:eExpt.No. 1 1506 1506 30.32 5.45e-08 ***
## Residuals 599 29758 50
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1]
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.2883 -4.2353 0.1126 4.0307 22.2719
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.41492 1.51465 37.246 < 2e-16 ***
## Criteria.Entry.No.02 -2.07131 1.37340 -1.508 0.132048
## Criteria.Entry.No.03 -5.22329 1.37340 -3.803 0.000158 ***
## Criteria.Entry.No.04 -15.17534 1.37340 -11.049 < 2e-16 ***
## Criteria.Entry.No.05 3.88492 1.37340 2.829 0.004833 **
## Criteria.Entry.No.06 6.35209 1.37340 4.625 4.61e-06 ***
## Criteria.Entry.No.07 -4.27983 1.37340 -3.116 0.001921 **
## Criteria.Entry.No.08 -7.26744 1.37340 -5.292 1.71e-07 ***
## Criteria.Entry.No.09 -2.75782 1.37340 -2.008 0.045097 *
## Criteria.Entry.No.10 0.58502 1.37340 0.426 0.670291
## Criteria.Entry.No.11 -0.76620 1.37340 -0.558 0.577135
## Criteria.Entry.No.12 -0.18131 1.37340 -0.132 0.895020
## Expt.No.CPT:2007:Brookings -8.62533 1.70102 -5.071 5.32e-07 ***
## Expt.No.CPT:2007:DLakesPea 2.87393 1.46212 1.966 0.049814 *
## Expt.No.CPT:2007:Hayes -1.30184 1.43624 -0.906 0.365081
## Expt.No.CPT:2007:Kennebec -9.55410 1.75681 -5.438 7.89e-08 ***
## Expt.No.CPT:2007:Martin -20.40688 2.60801 -7.825 2.37e-14 ***
## Expt.No.CPT:2007:Onida 2.03001 1.44585 1.404 0.160840
## Expt.No.CPT:2007:Platte 4.91871 1.52311 3.229 0.001310 **
## Expt.No.CPT:2007:Selby 0.69750 1.43142 0.487 0.626244
## Expt.No.CPT:2007:Sturgis -25.11669 3.04164 -8.258 9.81e-16 ***
## Expt.No.CPT:2007:Wall -7.14698 1.62082 -4.409 1.23e-05 ***
## Expt.No.CPT:2007:Watertown -5.17726 1.53287 -3.378 0.000780 ***
## Expt.No.CPT:2007:Winner -10.86913 1.84208 -5.900 6.12e-09 ***
## Criteria.Entry.No.01:eExpt.No. 0.35652 0.17219 2.071 0.038839 *
## Criteria.Entry.No.02:eExpt.No. 0.04164 0.17219 0.242 0.808984
## Criteria.Entry.No.03:eExpt.No. -0.46920 0.17219 -2.725 0.006623 **
## Criteria.Entry.No.04:eExpt.No. -0.50687 0.17219 -2.944 0.003371 **
## Criteria.Entry.No.05:eExpt.No. 0.11684 0.17219 0.679 0.497673
## Criteria.Entry.No.06:eExpt.No. 0.17244 0.17219 1.001 0.317004
## Criteria.Entry.No.07:eExpt.No. -0.09965 0.17219 -0.579 0.562979
## Criteria.Entry.No.08:eExpt.No. -0.32989 0.17219 -1.916 0.055863 .
## Criteria.Entry.No.09:eExpt.No. -0.11044 0.17219 -0.641 0.521511
## Criteria.Entry.No.10:eExpt.No. -0.08524 0.17219 -0.495 0.620746
## Criteria.Entry.No.11:eExpt.No. -0.17273 0.17219 -1.003 0.316215
## Criteria.Entry.No.12:eExpt.No. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.003 on 589 degrees of freedom
## Multiple R-squared: 0.6735, Adjusted R-squared: 0.6547
## F-statistic: 35.73 on 34 and 589 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.2883 -4.2353 0.1126 4.0307 22.2719
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Criteria.Entry.No.01 50.4397 0.9622 52.421 < 2e-16 ***
## Criteria.Entry.No.02 48.3684 0.9622 50.269 < 2e-16 ***
## Criteria.Entry.No.03 45.2164 0.9622 46.993 < 2e-16 ***
## Criteria.Entry.No.04 35.2643 0.9622 36.650 < 2e-16 ***
## Criteria.Entry.No.05 54.3246 0.9622 56.459 < 2e-16 ***
## Criteria.Entry.No.06 56.7918 0.9622 59.023 < 2e-16 ***
## Criteria.Entry.No.07 46.1599 0.9622 47.973 < 2e-16 ***
## Criteria.Entry.No.08 43.1722 0.9622 44.868 < 2e-16 ***
## Criteria.Entry.No.09 47.6819 0.9622 49.555 < 2e-16 ***
## Criteria.Entry.No.10 51.0247 0.9622 53.029 < 2e-16 ***
## Criteria.Entry.No.11 49.6735 0.9622 51.625 < 2e-16 ***
## Criteria.Entry.No.12 50.2584 0.9622 52.233 < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No. 1.4471 0.1206 11.995 < 2e-16 ***
## Criteria.Entry.No.02:eExpt.No. 1.1322 0.1206 9.385 < 2e-16 ***
## Criteria.Entry.No.03:eExpt.No. 0.6214 0.1206 5.151 3.53e-07 ***
## Criteria.Entry.No.04:eExpt.No. 0.5837 0.1206 4.838 1.67e-06 ***
## Criteria.Entry.No.05:eExpt.No. 1.2074 0.1206 10.009 < 2e-16 ***
## Criteria.Entry.No.06:eExpt.No. 1.2630 0.1206 10.470 < 2e-16 ***
## Criteria.Entry.No.07:eExpt.No. 0.9909 0.1206 8.214 1.32e-15 ***
## Criteria.Entry.No.08:eExpt.No. 0.7607 0.1206 6.305 5.57e-10 ***
## Criteria.Entry.No.09:eExpt.No. 0.9801 0.1206 8.125 2.57e-15 ***
## Criteria.Entry.No.10:eExpt.No. 1.0053 0.1206 8.333 5.36e-16 ***
## Criteria.Entry.No.11:eExpt.No. 0.9178 0.1206 7.608 1.08e-13 ***
## Criteria.Entry.No.12:eExpt.No. 1.0905 0.1206 9.040 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.938 on 600 degrees of freedom
## Multiple R-squared: 0.9812, Adjusted R-squared: 0.9805
## F-statistic: 1306 on 24 and 600 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 12 1467088 122257 2539.48 <2e-16 ***
## Criteria.Entry.No.:eExpt.No. 12 42077 3506 72.83 <2e-16 ***
## Residuals 600 28886 48
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 17509 1592 32.456 < 2e-16 ***
## Expt.No. 12 39698 3308 67.456 < 2e-16 ***
## Criteria.Entry.No.:eExpt.No. 11 2378 216 4.409 2.19e-06 ***
## Residuals 589 28886 49
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
## Estimate Std. Error t value
## Criteria.Entry.No.01:eExpt.No. 1.4470667 0.1206344 3.70596311
## Criteria.Entry.No.02:eExpt.No. 1.1321911 0.1206344 1.09579923
## Criteria.Entry.No.03:eExpt.No. 0.6213510 0.1206344 -3.13881424
## Criteria.Entry.No.04:eExpt.No. 0.5836777 0.1206344 -3.45110697
## Criteria.Entry.No.05:eExpt.No. 1.2073912 0.1206344 1.71917068
## Criteria.Entry.No.06:eExpt.No. 1.2629921 0.1206344 2.18007496
## Criteria.Entry.No.07:eExpt.No. 0.9908940 0.1206344 -0.07548408
## Criteria.Entry.No.08:eExpt.No. 0.7606544 0.1206344 -1.98405710
## Criteria.Entry.No.09:eExpt.No. 0.9801060 0.1206344 -0.16491163
## Criteria.Entry.No.10:eExpt.No. 1.0053054 0.1206344 0.04397952
## Criteria.Entry.No.11:eExpt.No. 0.9178223 0.1206344 -0.68121274
## Criteria.Entry.No.12:eExpt.No. 1.0905481 0.1206344 0.75059926
## Pr(>|t|)
## Criteria.Entry.No.01:eExpt.No. 0.0001150347
## Criteria.Entry.No.02:eExpt.No. 0.1368031433
## Criteria.Entry.No.03:eExpt.No. 0.0008898051
## Criteria.Entry.No.04:eExpt.No. 0.0002987639
## Criteria.Entry.No.05:eExpt.No. 0.0430495326
## Criteria.Entry.No.06:eExpt.No. 0.0148199154
## Criteria.Entry.No.07:eExpt.No. 0.4699273624
## Criteria.Entry.No.08:eExpt.No. 0.0238523464
## Criteria.Entry.No.09:eExpt.No. 0.4345345426
## Criteria.Entry.No.10:eExpt.No. 0.4824676823
## Criteria.Entry.No.11:eExpt.No. 0.2479998550
## Criteria.Entry.No.12:eExpt.No. 0.2265940614
## [1]
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 9.901533
## [1] Interaction sd Value:
## [1] 6.172434
## [1] Error sd Value:
## [1] 4.125639
## [1] Pairs:
## [[1]]
## [1] 4 1
##
## [[2]]
## [1] 1 8
##
## [[3]]
## [1] 4 8
##
## [[4]]
## [1] 1 9
##
## [[5]]
## [1] 2 9
##
## [[6]]
## [1] 3 9
##
## [[7]]
## [1] 4 9
##
## [[8]]
## [1] 6 9
##
## [[9]]
## [1] 7 9
##
## [[10]]
## [1] 4 10
##
## [[11]]
## [1] 3 11
##
## [[12]]
## [1] 4 11
##
## [[13]]
## [1] 5 11
##
## [[14]]
## [1] 5 12
##
## [[15]]
## [1] 6 12
##
## [[16]]
## [1] 7 12
##
## [1]
## [1]gyb.res <- standard.sensitivity.plot(gy.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
outliers=2,
method="ave",
plot.outliers=TRUE,legend.columns=3)
gy2.res <- standard.sensitivity.plot(gy.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
outliers=2.4,
dual.dendrogram=TRUE,
method="ave",
plot.outliers=TRUE,legend.columns=3)
means.matrix <- tapply(gy.dat$Plot.Mean,list(gy.dat$Criteria.Entry.No.,gy.dat$Expt.No.),mean)
decomp <- decompose.means.table(means.matrix)
txt.matrix <- decomp$gamma
mean(unlist(txt.matrix),na.rm=TRUE)## [1] -2.095165e-15max <- sd(unlist(txt.matrix),na.rm=TRUE)
norm.mat <- abs(txt.matrix)
crit <- 3*max
gy.means$means.table - means.matrix## CPT:2007:Bison CPT:2007:Brookings CPT:2007:DLakesPea CPT:2007:Hayes
## 01 5.258016e-13 -1.492140e-13 8.526513e-14 -1.776357e-13
## 02 4.618528e-13 -1.065814e-13 0.000000e+00 -2.131628e-13
## 03 3.055334e-13 -4.973799e-14 1.492140e-13 -1.492140e-13
## 04 6.679102e-13 5.329071e-14 7.105427e-15 -1.563194e-13
## 05 -3.410605e-13 -1.065814e-13 -7.105427e-15 -2.273737e-13
## 06 1.186606e-12 -1.421085e-13 5.684342e-14 -2.344791e-13
## 07 0.000000e+00 -1.421085e-14 0.000000e+00 -2.060574e-13
## 08 4.263256e-14 -5.684342e-14 7.105427e-14 -1.847411e-13
## 09 2.131628e-14 -2.842171e-14 8.526513e-14 -1.634248e-13
## 10 4.192202e-13 -9.237056e-14 4.263256e-14 -1.847411e-13
## 11 1.421085e-13 -8.526513e-14 1.136868e-13 -1.634248e-13
## 12 2.060574e-13 -1.065814e-13 3.552714e-14 -1.918465e-13
## CPT:2007:Kennebec CPT:2007:Martin CPT:2007:Onida CPT:2007:Platte
## 01 1.705303e-13 -4.725109e-13 1.989520e-13 2.557954e-13
## 02 3.197442e-13 -4.689582e-13 1.989520e-13 2.629008e-13
## 03 3.836931e-13 -4.121148e-13 2.131628e-13 2.273737e-13
## 04 4.369838e-13 -3.907985e-13 2.913225e-13 2.486900e-13
## 05 3.197442e-13 -4.547474e-13 2.060574e-13 2.415845e-13
## 06 3.481659e-13 -4.263256e-13 2.202682e-13 2.415845e-13
## 07 3.836931e-13 -4.547474e-13 2.771117e-13 2.842171e-13
## 08 3.623768e-13 -4.760636e-13 1.918465e-13 2.984279e-13
## 09 4.121148e-13 -4.263256e-13 2.486900e-13 2.984279e-13
## 10 3.979039e-13 -4.547474e-13 2.344791e-13 2.344791e-13
## 11 3.979039e-13 -4.405365e-13 2.202682e-13 2.984279e-13
## 12 3.907985e-13 -4.689582e-13 2.415845e-13 2.984279e-13
## CPT:2007:Selby CPT:2007:Sturgis CPT:2007:Wall CPT:2007:Watertown
## 01 2.415845e-13 4.263256e-14 1.776357e-13 1.492140e-13
## 02 1.705303e-13 -4.263256e-14 1.421085e-13 1.350031e-13
## 03 3.055334e-13 -2.842171e-14 1.563194e-13 1.847411e-13
## 04 2.167155e-13 1.065814e-14 2.202682e-13 2.273737e-13
## 05 1.847411e-13 -6.394885e-14 1.634248e-13 1.705303e-13
## 06 2.557954e-13 -4.973799e-14 1.918465e-13 1.705303e-13
## 07 2.486900e-13 -3.197442e-14 1.207923e-13 1.350031e-13
## 08 2.060574e-13 -2.486900e-14 1.563194e-13 1.563194e-13
## 09 2.415845e-13 -1.065814e-14 1.989520e-13 2.202682e-13
## 10 2.486900e-13 -2.131628e-14 1.705303e-13 1.918465e-13
## 11 2.273737e-13 -7.105427e-15 1.705303e-13 2.131628e-13
## 12 2.486900e-13 -1.421085e-14 1.918465e-13 1.989520e-13
## CPT:2007:Winner
## 01 1.421085e-13
## 02 1.492140e-13
## 03 1.563194e-13
## 04 2.060574e-13
## 05 1.421085e-13
## 06 1.705303e-13
## 07 1.421085e-13
## 08 1.705303e-13
## 09 1.847411e-13
## 10 1.634248e-13
## 11 1.918465e-13
## 12 2.060574e-13gy.res$cluster$score/gy.res$add.cluster$score## [1] 1.3927179 1.2256504 1.0296006 1.2545966 0.9612729 0.9204759
## [7] 0.8777299 0.2101115 0.4671611 77.5177481 0.9335306 0.9547280gy.res$cluster$clusters## [1] 1 1 2 1 1 3 2 2 2 3 1 1 1gy.res$add.cluster$clusters## 1 2 3 4 5 6 7 8 9 10 11 12 13
## 1 2 1 1 2 3 1 1 1 3 2 2 2gy.res$cluster$means.hc$height## [1] 12.75757 16.01341 19.38159 19.76017 23.51187 24.68833 26.87330
## [8] 34.53185 34.78175 47.55139 62.18434 103.29494gy.res$add.cluster$means.hc$height## [1] 2.215582 2.680709 2.950214 6.256760 6.350852 7.127390 9.175900
## [8] 14.960588 18.080083 19.759451 50.149726 95.406771gy.res$cluster$means.hc$height/gy.res$add.cluster$means.hc$height## [1] 5.758115 5.973574 6.569555 3.158211 3.702160 3.463867 2.928683
## [8] 2.308188 1.923760 2.406514 1.239974 1.082679gy.res$cluster$means.hc$order## [1] 6 10 9 8 3 7 11 1 4 12 5 2 13gy.res$add.cluster$means.hc$order## [1] 6 10 11 12 13 2 5 4 1 9 8 3 7gy.res$cluster$means.hc$merge## [,1] [,2]
## [1,] -2 -13
## [2,] -1 -4
## [3,] -3 -7
## [4,] -5 1
## [5,] -6 -10
## [6,] -8 3
## [7,] -11 2
## [8,] -9 6
## [9,] -12 4
## [10,] 7 9
## [11,] 8 10
## [12,] 5 11gy.res$add.cluster$means.hc$merge## [,1] [,2]
## [1,] -1 -9
## [2,] -3 -7
## [3,] -2 -5
## [4,] -11 -12
## [5,] -4 1
## [6,] -13 3
## [7,] -8 2
## [8,] -6 -10
## [9,] 4 6
## [10,] 5 7
## [11,] 9 10
## [12,] 8 11gy.res$cluster$means.hc$merge==gy.res$add.cluster$means.hc$merge## [,1] [,2]
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,] FALSE FALSE
## [5,] FALSE FALSE
## [6,] FALSE TRUE
## [7,] FALSE TRUE
## [8,] FALSE FALSE
## [9,] FALSE FALSE
## [10,] FALSE FALSE
## [11,] FALSE TRUE
## [12,] FALSE TRUEtdf.tbl <- anova(gy.res$tdf$multiplicative.lm)
aov.tbl <- gy.res$aov
tdf.tbl## Analysis of Variance Table
##
## Response: Plot.Mean
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 17509 1591.7 32.039 < 2.2e-16 ***
## Expt.No. 12 39698 3308.2 66.590 < 2.2e-16 ***
## eCriteria.Entry.No.:eExpt.No. 1 1506 1506.1 30.316 5.451e-08 ***
## Residuals 599 29758 49.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1aov.tbl## Analysis of Variance Table
##
## Response: Plot.Mean
## Df Sum Sq Mean Sq F value Pr(>F)
## Expt.No. 12 39698 3308.2 194.3594 < 2.2e-16 ***
## Criteria.Entry.No. 11 17509 1591.7 93.5136 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132 19964 151.2 8.8856 < 2.2e-16 ***
## Expt.No.:Rep.No. 39 3998 102.5 6.0232 < 2.2e-16 ***
## Residuals 429 7302 17.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1recompute.tdf.aov(tdf.tbl,aov.tbl)## Analysis of Variance Table
##
## Response: Plot.Mean
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 17509 1591.7 32.0391 < 2.2e-16 ***
## Expt.No. 12 39698 3308.2 66.5903 < 2.2e-16 ***
## eCriteria.Entry.No.:eExpt.No. 1 1506 1506.1 22.9645 2.536e-05 ***
## Residuals 38 2492 65.6 3.8531 3.647e-12 ***
## Residuals1 429 7302 17.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1last = dim(aov.tbl)[1] last.row <- aov.tbl[last,] tdf.last <- dim(tdf.tbl)[1] colnames(last.row) <- colnames(tdf.tbl) tdf.tbl <- rbind(tdf.tbl,last.row) #compute interaction residuals by subtracting 1df row from txt row tdf.tbl[tdf.last,] <- aov.tbl[last-1,] - tdf.tbl[tdf.last-1,] #recompute residuals tdf.tbl[tdf.last,3] <- tdf.tbl[tdf.last,2]/tdf.tbl[tdf.last,1] #test treatment:trial against interaction residual tdf.tbl[tdf.last-1,4] <- tdf.tbl[tdf.last-1,3]/tdf.tbl[tdf.last,3] tdf.tbl[tdf.last-1,5] <- 1-pf(tdf.tbl[tdf.last-1,4],tdf.tbl[tdf.last-1,1],tdf.tbl[tdf.last,1])
#test interaction residual against experimental residual tdf.tbl[tdf.last,4] <- tdf.tbl[tdf.last,3]/last.row[3] tdf.tbl[tdf.last,5] <- 1-pf(tdf.tbl[tdf.last,4],tdf.tbl[tdf.last,1],as.numeric(last.row[1]))
return(tdf.tbl)
```
tw.res <- standard.sensitivity.plot(tw.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
dual.dendrogram=TRUE,
plot.outliers=TRUE,legend.columns=3)
print.stdplot(tw.res)## [1] ----------------------------------------------------
## [1] Effects
## [,1]
## 1 3.8815922
## 2 -0.3701871
## 3 -0.6880950
## 4 5.3024252
## 5 -1.3522327
## 6 2.4545091
## 7 -2.3627820
## 8 -1.6500748
## 9 -4.1854911
## 10 3.8003419
## 11 -1.3228814
## 12 -0.6975722
## 13 -2.8095520
## [,1]
## 1 0.4520830
## 2 -2.0979172
## 3 -0.2229163
## 4 2.5020831
## 5 -0.2979170
## 6 1.1770833
## 7 2.0270837
## 8 -1.6729161
## 9 0.9770845
## 10 -2.7229163
## 11 -0.2729174
## 12 0.1520828
## [1] Means
## [,1]
## 1 63.07292
## 2 59.23529
## 3 56.57618
## 4 61.06368
## 5 57.52618
## 6 62.64404
## 7 56.41423
## 8 54.48255
## 9 55.17046
## 10 64.38054
## 11 58.68569
## 12 56.51488
## 13 53.72145
## [,1]
## 1 59.19784
## 2 59.07935
## 3 57.46056
## 4 57.10709
## 5 60.81155
## 6 60.64901
## 7 59.35348
## 8 55.38728
## 9 60.74249
## 10 57.26328
## 11 57.82618
## 12 56.18782
## [1] Row Col Means
## [1] 63.07292 57.61053 57.08760 61.85208 53.72670 59.85000 57.23229
## [8] 55.63458 55.92292 61.14583 58.96981 59.97125 57.41156
## X1 X2 X3 X4 X5 X6 X7 X8
## 59.19784 59.07935 57.46056 57.10709 60.81155 60.64901 59.35348 55.38728
## X9 X10 X11 X12
## 60.74249 57.26328 57.82618 56.18782
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
##
## Response: Plot.Mean
## Df Sum Sq Mean Sq F value Pr(>F)
## Expt.No. 12 4128.3 344.02 168.3919 < 2.2e-16 ***
## Criteria.Entry.No. 11 1880.3 170.93 83.6688 < 2.2e-16 ***
## Expt.No.:Criteria.Entry.No. 132 1631.9 12.36 6.0515 < 2.2e-16 ***
## Expt.No.:Rep.No. 39 301.6 7.73 3.7854 4.862e-12 ***
## Residuals 425 868.3 2.04
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula:
## Plot.Mean ~ Expt.No. + (1 | Expt.No./Rep.No.) + (1 | Expt.No.:Criteria.Entry.No.)
## Data: plot.dat
##
## REML criterion at convergence: 2613.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4708 -0.4532 0.0575 0.5014 2.6909
##
## Random effects:
## Groups Name Variance Std.Dev.
## Expt.No.:Criteria.Entry.No. (Intercept) 5.6585 2.3788
## Rep.No.:Expt.No. (Intercept) 0.4781 0.6914
## Expt.No. (Intercept) 7.4666 2.7325
## Residual 2.0446 1.4299
## Number of obs: 620, groups:
## Expt.No.:Criteria.Entry.No., 156; Rep.No.:Expt.No., 52; Expt.No., 13
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 63.073 2.846 22.161
## Expt.No.CPT:2007:Brookings -5.383 4.026 -1.337
## Expt.No.CPT:2007:DLakesPea -5.985 4.025 -1.487
## Expt.No.CPT:2007:Hayes -1.221 4.025 -0.303
## Expt.No.CPT:2007:Kennebec -9.357 4.025 -2.325
## Expt.No.CPT:2007:Martin -3.223 4.025 -0.801
## Expt.No.CPT:2007:Onida -5.841 4.025 -1.451
## Expt.No.CPT:2007:Platte -7.438 4.025 -1.848
## Expt.No.CPT:2007:Selby -7.150 4.025 -1.776
## Expt.No.CPT:2007:Sturgis -1.927 4.025 -0.479
## Expt.No.CPT:2007:Wall -4.103 4.025 -1.019
## Expt.No.CPT:2007:Watertown -3.102 4.025 -0.771
## Expt.No.CPT:2007:Winner -5.661 4.025 -1.407##
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(summary(fit$lmer), correlation=TRUE) or
## vcov(summary(fit$lmer)) if you need it## [1]
## [1] Stability
## [1] ----------------------------------------------------
## Treatment Slope Intercept Mean SD b
## 1 1 1.0236239 -0.6044865 59.19784 3.206041 0.023623936
## 2 2 0.5756150 25.4506800 59.07935 1.786156 -0.424385033
## 3 3 1.4578990 -27.7130516 57.46056 4.173253 0.457899021
## 4 4 1.6812709 -41.1163899 57.10709 4.908317 0.681270932
## 5 5 0.5923172 26.2070972 60.81155 2.060720 -0.407682801
## 6 6 0.5074963 30.9999788 60.64901 2.078896 -0.492503662
## 7 7 1.0076033 0.4871182 59.35348 3.057007 0.007603260
## 8 8 1.3668135 -24.4649125 55.38728 3.797264 0.366813461
## 9 9 0.5600023 28.0259437 60.74249 1.988947 -0.439997720
## 10 10 1.0024725 -1.3033282 57.26328 2.898771 0.002472472
## 11 11 0.8397078 8.7686355 57.82618 2.473374 -0.160292179
## 12 12 1.3851783 -24.7372847 56.18782 3.860661 0.385178314
## Pb bR2
## 1 0.900928919 1.473171e-03
## 2 0.001438911 6.180498e-01
## 3 0.016789197 4.188968e-01
## 4 0.009307985 4.736197e-01
## 5 0.018238667 4.108484e-01
## 6 0.017495975 4.149003e-01
## 7 0.962931685 2.054539e-04
## 8 0.006547976 5.040948e-01
## 9 0.011892635 4.514403e-01
## 10 0.984054800 3.799709e-05
## 11 0.188308310 1.517212e-01
## 12 0.006984747 4.986186e-01
## [1]
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.865 -1.207 0.117 1.301 5.082
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 63.84375 0.39430 161.915 < 2e-16 ***
## Criteria.Entry.No.02 -0.11849 0.39425 -0.301 0.763873
## Criteria.Entry.No.03 -1.73728 0.39425 -4.407 1.25e-05 ***
## Criteria.Entry.No.04 -1.97890 0.40062 -4.940 1.02e-06 ***
## Criteria.Entry.No.05 1.61371 0.39425 4.093 4.84e-05 ***
## Criteria.Entry.No.06 1.45118 0.39425 3.681 0.000254 ***
## Criteria.Entry.No.07 0.15564 0.39425 0.395 0.693144
## Criteria.Entry.No.08 -3.81055 0.39425 -9.665 < 2e-16 ***
## Criteria.Entry.No.09 1.54465 0.39425 3.918 9.97e-05 ***
## Criteria.Entry.No.10 -1.93456 0.39425 -4.907 1.20e-06 ***
## Criteria.Entry.No.11 -1.42539 0.39621 -3.598 0.000348 ***
## Criteria.Entry.No.12 -3.01001 0.39425 -7.635 9.05e-14 ***
## Expt.No.CPT:2007:Brookings -5.34123 0.41753 -12.792 < 2e-16 ***
## Expt.No.CPT:2007:DLakesPea -5.98531 0.41034 -14.586 < 2e-16 ***
## Expt.No.CPT:2007:Hayes -1.22083 0.41034 -2.975 0.003047 **
## Expt.No.CPT:2007:Kennebec -9.40444 0.41256 -22.795 < 2e-16 ***
## Expt.No.CPT:2007:Martin -3.22292 0.41034 -7.854 1.89e-14 ***
## Expt.No.CPT:2007:Onida -5.84062 0.41034 -14.233 < 2e-16 ***
## Expt.No.CPT:2007:Platte -7.43833 0.41034 -18.127 < 2e-16 ***
## Expt.No.CPT:2007:Selby -7.15000 0.41034 -17.424 < 2e-16 ***
## Expt.No.CPT:2007:Sturgis -1.92708 0.41034 -4.696 3.29e-06 ***
## Expt.No.CPT:2007:Wall -4.10310 0.41034 -9.999 < 2e-16 ***
## Expt.No.CPT:2007:Watertown -3.10167 0.41034 -7.559 1.55e-13 ***
## Expt.No.CPT:2007:Winner -5.66135 0.41034 -13.797 < 2e-16 ***
## eCriteria.Entry.No.:eExpt.No. -0.17781 0.01793 -9.915 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.01 on 595 degrees of freedom
## Multiple R-squared: 0.7271, Adjusted R-squared: 0.7161
## F-statistic: 66.05 on 24 and 595 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 1870 170.0 42.06 <2e-16 ***
## Expt.No. 12 4139 344.9 85.34 <2e-16 ***
## eCriteria.Entry.No.:eExpt.No. 1 397 397.3 98.31 <2e-16 ***
## Residuals 595 2405 4.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1]
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.737 -1.138 0.085 1.313 5.415
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 65.62016 0.59968 109.426 < 2e-16 ***
## Criteria.Entry.No.02 -0.11849 0.38063 -0.311 0.755693
## Criteria.Entry.No.03 -1.73728 0.38063 -4.564 6.11e-06 ***
## Criteria.Entry.No.04 -1.99941 0.38681 -5.169 3.24e-07 ***
## Criteria.Entry.No.05 1.61371 0.38063 4.240 2.60e-05 ***
## Criteria.Entry.No.06 1.45118 0.38063 3.813 0.000152 ***
## Criteria.Entry.No.07 0.15564 0.38063 0.409 0.682757
## Criteria.Entry.No.08 -3.81055 0.38063 -10.011 < 2e-16 ***
## Criteria.Entry.No.09 1.54465 0.38063 4.058 5.62e-05 ***
## Criteria.Entry.No.10 -1.93456 0.38063 -5.083 5.02e-07 ***
## Criteria.Entry.No.11 -1.40095 0.38265 -3.661 0.000274 ***
## Criteria.Entry.No.12 -3.01001 0.38063 -7.908 1.31e-14 ***
## Expt.No.CPT:2007:Brookings -7.40290 0.66714 -11.097 < 2e-16 ***
## Expt.No.CPT:2007:DLakesPea -8.27512 0.71673 -11.546 < 2e-16 ***
## Expt.No.CPT:2007:Hayes -1.68789 0.41448 -4.072 5.30e-05 ***
## Expt.No.CPT:2007:Kennebec -12.97131 1.01758 -12.747 < 2e-16 ***
## Expt.No.CPT:2007:Martin -4.45591 0.51029 -8.732 < 2e-16 ***
## Expt.No.CPT:2007:Onida -8.07508 0.70475 -11.458 < 2e-16 ***
## Expt.No.CPT:2007:Platte -10.28402 0.84140 -12.223 < 2e-16 ***
## Expt.No.CPT:2007:Selby -9.88538 0.81612 -12.113 < 2e-16 ***
## Expt.No.CPT:2007:Sturgis -2.66433 0.44038 -6.050 2.59e-09 ***
## Expt.No.CPT:2007:Wall -5.67283 0.56974 -9.957 < 2e-16 ***
## Expt.No.CPT:2007:Watertown -4.28827 0.50275 -8.530 < 2e-16 ***
## Expt.No.CPT:2007:Winner -7.82722 0.69002 -11.343 < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No. -0.36266 0.14736 -2.461 0.014142 *
## Criteria.Entry.No.02:eExpt.No. -0.80570 0.14736 -5.468 6.77e-08 ***
## Criteria.Entry.No.03:eExpt.No. 0.07421 0.14736 0.504 0.614739
## Criteria.Entry.No.04:eExpt.No. 0.28564 0.14753 1.936 0.053331 .
## Criteria.Entry.No.05:eExpt.No. -0.78867 0.14736 -5.352 1.25e-07 ***
## Criteria.Entry.No.06:eExpt.No. -0.87148 0.14736 -5.914 5.68e-09 ***
## Criteria.Entry.No.07:eExpt.No. -0.37879 0.14736 -2.570 0.010402 *
## Criteria.Entry.No.08:eExpt.No. -0.02020 0.14736 -0.137 0.891030
## Criteria.Entry.No.09:eExpt.No. -0.81980 0.14736 -5.563 4.03e-08 ***
## Criteria.Entry.No.10:eExpt.No. -0.37855 0.14736 -2.569 0.010450 *
## Criteria.Entry.No.11:eExpt.No. -0.52487 0.14999 -3.499 0.000502 ***
## Criteria.Entry.No.12:eExpt.No. NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.941 on 585 degrees of freedom
## Multiple R-squared: 0.7499, Adjusted R-squared: 0.7353
## F-statistic: 51.59 on 34 and 585 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7353 -1.1389 0.0856 1.3044 5.4255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Criteria.Entry.No.01 59.1978 0.2667 222.003 < 2e-16 ***
## Criteria.Entry.No.02 59.0793 0.2667 221.558 < 2e-16 ***
## Criteria.Entry.No.03 57.4606 0.2667 215.488 < 2e-16 ***
## Criteria.Entry.No.04 57.2004 0.2747 208.206 < 2e-16 ***
## Criteria.Entry.No.05 60.8115 0.2667 228.054 < 2e-16 ***
## Criteria.Entry.No.06 60.6490 0.2667 227.445 < 2e-16 ***
## Criteria.Entry.No.07 59.3535 0.2667 222.586 < 2e-16 ***
## Criteria.Entry.No.08 55.3873 0.2667 207.712 < 2e-16 ***
## Criteria.Entry.No.09 60.7425 0.2667 227.795 < 2e-16 ***
## Criteria.Entry.No.10 57.2633 0.2667 214.748 < 2e-16 ***
## Criteria.Entry.No.11 57.7966 0.2694 214.507 < 2e-16 ***
## Criteria.Entry.No.12 56.1878 0.2667 210.715 < 2e-16 ***
## Criteria.Entry.No.01:eExpt.No. 1.0194 0.1032 9.874 < 2e-16 ***
## Criteria.Entry.No.02:eExpt.No. 0.5763 0.1032 5.583 3.60e-08 ***
## Criteria.Entry.No.03:eExpt.No. 1.4562 0.1032 14.106 < 2e-16 ***
## Criteria.Entry.No.04:eExpt.No. 1.6675 0.1035 16.117 < 2e-16 ***
## Criteria.Entry.No.05:eExpt.No. 0.5934 0.1032 5.748 1.45e-08 ***
## Criteria.Entry.No.06:eExpt.No. 0.5105 0.1032 4.945 9.89e-07 ***
## Criteria.Entry.No.07:eExpt.No. 1.0032 0.1032 9.718 < 2e-16 ***
## Criteria.Entry.No.08:eExpt.No. 1.3618 0.1032 13.192 < 2e-16 ***
## Criteria.Entry.No.09:eExpt.No. 0.5622 0.1032 5.446 7.54e-08 ***
## Criteria.Entry.No.10:eExpt.No. 1.0035 0.1032 9.720 < 2e-16 ***
## Criteria.Entry.No.11:eExpt.No. 0.8574 0.1068 8.025 5.42e-15 ***
## Criteria.Entry.No.12:eExpt.No. 1.3820 0.1032 13.387 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.923 on 596 degrees of freedom
## Multiple R-squared: 0.999, Adjusted R-squared: 0.9989
## F-statistic: 2.394e+04 on 24 and 596 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 12 2119788 176649 47776.3 <2e-16 ***
## Criteria.Entry.No.:eExpt.No. 12 4737 395 106.8 <2e-16 ***
## Residuals 596 2204 4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## Criteria.Entry.No. 11 1870 170.0 45.13 <2e-16 ***
## Expt.No. 12 4139 344.9 91.56 <2e-16 ***
## Criteria.Entry.No.:eExpt.No. 11 598 54.4 14.44 <2e-16 ***
## Residuals 585 2204 3.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
## Estimate Std. Error t value
## Criteria.Entry.No.01:eExpt.No. 1.0193656 0.1032350 0.18758810
## Criteria.Entry.No.02:eExpt.No. 0.5763251 0.1032350 -4.10398682
## Criteria.Entry.No.03:eExpt.No. 1.4562332 0.1032350 4.41936798
## Criteria.Entry.No.04:eExpt.No. 1.6674667 0.1034591 6.45150610
## Criteria.Entry.No.05:eExpt.No. 0.5933559 0.1032350 -3.93901529
## Criteria.Entry.No.06:eExpt.No. 0.5105451 0.1032350 -4.74117384
## Criteria.Entry.No.07:eExpt.No. 1.0032367 0.1032350 0.03135295
## Criteria.Entry.No.08:eExpt.No. 1.3618265 0.1032350 3.50488360
## Criteria.Entry.No.09:eExpt.No. 0.5622276 0.1032350 -4.24054415
## Criteria.Entry.No.10:eExpt.No. 1.0034753 0.1032350 0.03366446
## Criteria.Entry.No.11:eExpt.No. 0.8573542 0.1068354 -1.33519302
## Criteria.Entry.No.12:eExpt.No. 1.3820238 0.1032350 3.70052772
## Pr(>|t|)
## Criteria.Entry.No.01:eExpt.No. 4.256317e-01
## Criteria.Entry.No.02:eExpt.No. 2.313376e-05
## Criteria.Entry.No.03:eExpt.No. 5.880879e-06
## Criteria.Entry.No.04:eExpt.No. 1.146625e-10
## Criteria.Entry.No.05:eExpt.No. 4.574919e-05
## Criteria.Entry.No.06:eExpt.No. 1.330452e-06
## Criteria.Entry.No.07:eExpt.No. 4.874993e-01
## Criteria.Entry.No.08:eExpt.No. 2.455515e-04
## Criteria.Entry.No.09:eExpt.No. 1.292144e-05
## Criteria.Entry.No.10:eExpt.No. 4.865780e-01
## Criteria.Entry.No.11:eExpt.No. 9.116146e-02
## Criteria.Entry.No.12:eExpt.No. 1.175387e-04
## [1]
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 4.287986
## [1] Interaction sd Value:
## [1] 1.769951
## [1] Error sd Value:
## [1] 1.429329
## [1] Pairs:
## [[1]]
## [1] 4 9
##
## [[2]]
## [1] 4 10
##
## [1]
## [1]tw.res$cluster$score/tw.res$add.cluster$score## [1] 1.2259743 0.9697232 0.9300447 0.8278188 0.8531172 0.8305974 0.8721844
## [8] 3.7475335 1.8639613 0.2142266 1.6386883 0.9722437tw.res <- standard.sensitivity.plot(tw.dat,
response = response,
TreatmentName = TreatmentName,
TrialName = TrialName,
RepName=RepName,
dual.dendrogram=FALSE,
plot.outliers=TRUE,legend.columns=3)
gy.matrix <- data.frame(tapply(gy.dat$Plot.Mean,list(gy.dat$Expt.No.,gy.dat$Criteria.Entry.No.),mean))
gy.vector <- tapply(gy.dat$Plot.Mean,list(gy.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
gy.table <- plot.interaction.ARMST(gy.matrix, gy.vector, ylab='Treatment in Trial Mean',
regression=TRUE, main='GY', show.legend=TRUE,legend.pos=c(.01,.98),
legend.columns=4,lwd = 1
)
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
gy.hc <- plot.clusters.ARMST(gy.matrix, gy.vector, xlab='Trial Mean', ylab='')
par(fig = c(0, 1, 0, 1))
tw.matrix <- data.frame(tapply(tw.dat$Plot.Mean,list(tw.dat$Expt.No.,tw.dat$Criteria.Entry.No.),mean))
tw.vector <- tapply(tw.dat$Plot.Mean,list(tw.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
tw.table <- plot.interaction.ARMST(tw.matrix, tw.vector, ylab='Treatment in Trial Mean',
regression=TRUE, main='TW', show.legend=TRUE,legend.pos=c(.01,.98),
legend.columns=4,lwd = 1
)
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
tw.hc <- plot.clusters.ARMST(tw.matrix, tw.vector, xlab='Trial Mean', ylab='')
par(fig = c(0, 1, 0, 1))
hd.matrix <- data.frame(tapply(hd.dat$Plot.Mean,list(hd.dat$Expt.No.,hd.dat$Criteria.Entry.No.),mean))
hd.vector <- tapply(hd.dat$Plot.Mean,list(hd.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
hd.table <- plot.interaction.ARMST(hd.matrix, hd.vector, ylab='Treatment in Trial Mean',
regression=TRUE, main='HD', show.legend=TRUE,legend.pos=c(.01,.98),
legend.columns=4,lwd = 1
)
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
hd.hc <- plot.clusters.ARMST(hd.matrix, hd.vector, xlab='Trial Mean', ylab='')
par(fig = c(0, 1, 0, 1))
ht.matrix <- data.frame(tapply(ht.dat$Plot.Mean,list(ht.dat$Expt.No.,ht.dat$Criteria.Entry.No.),mean))
ht.vector <- tapply(ht.dat$Plot.Mean,list(ht.dat$Expt.No.),mean)
par(fig = c(0, 1, 0.4, 1), mar = (c(1, 4, 1, 1) + 0.1))
ht.table <- plot.interaction.ARMST(ht.matrix, ht.vector, ylab='Treatment in Trial Mean',
regression=TRUE, main='HT', show.legend=TRUE,legend.pos=c(.01,.98),
legend.columns=4,lwd = 1
)
par(fig=c(0,1,0,.4),mar=(c(5, 4, 0, 1) + 0.1), new=TRUE)
ht.hc <- plot.clusters.ARMST(ht.matrix, ht.vector, xlab='Trial Mean', ylab='')
par(fig = c(0, 1, 0, 1))library(agridat)
data(pacheco.soybean)
mixed.res <- standard.sensitivity.plot(pacheco.soybean,
response = "yield",
TreatmentName = "gen",
TrialName = "env",
dual.dendrogram=TRUE,
plot.outliers=TRUE,legend.columns=3)## Warning in anova.lm(base.lm): ANOVA F-tests on an essentially perfect fit
## are unreliable
print.stdplot(mixed.res)## [1] ----------------------------------------------------
## [1] Effects
## NULL
## NULL
## [1] Means
## [,1]
## 1 1756.278
## 2 2222.722
## 3 1910.444
## 4 1234.167
## 5 1682.556
## 6 854.500
## 7 3659.944
## 8 2214.444
## 9 2074.667
## 10 2724.278
## 11 2453.556
## [,1]
## 1 2457.727
## 2 2053.364
## 3 2181.455
## 4 2172.455
## 5 1736.364
## 6 2173.818
## 7 1860.000
## 8 1858.091
## 9 2053.182
## 10 2225.727
## 11 2258.364
## 12 2081.545
## 13 2085.455
## 14 1920.909
## 15 2159.545
## 16 2117.364
## 17 1922.727
## 18 1970.636
## [1] Row Col Means
## [1] 1756.278 2289.389 2185.389 1770.944 1659.167 1125.278 2592.500
## [8] 2400.278 2395.667 2456.778 2155.889
## X1 X2 X3 X4 X5 X6 X7 X8
## 2457.727 2053.364 2181.455 2172.455 1736.364 2173.818 1860.000 1858.091
## X9 X10 X11 X12 X13 X14 X15 X16
## 2053.182 2225.727 2258.364 2081.545 2085.455 1920.909 2159.545 2117.364
## X17 X18
## 1922.727 1970.636
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
##
## Response: yield
## Df Sum Sq Mean Sq F value Pr(>F)
## env 10 35202247 3520225
## gen 17 5599202 329365
## env:gen 170 13110345 77120
## Residuals 0 0
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: yield ~ env + (1 | env)
## Data: plot.dat
##
## REML criterion at convergence: 2715.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4589 -0.5756 -0.1965 0.5819 3.8459
##
## Random effects:
## Groups Name Variance Std.Dev.
## env (Intercept) 271980 521.5
## Residual 100051 316.3
## Number of obs: 198, groups: env, 11
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1756.28 526.82 3.334
## envE10 533.11 745.04 0.716
## envE11 429.11 745.04 0.576
## envE2 14.67 745.04 0.020
## envE3 -97.11 745.04 -0.130
## envE4 -631.00 745.04 -0.847
## envE5 836.22 745.04 1.122
## envE6 644.00 745.04 0.864
## envE7 639.39 745.04 0.858
## envE8 700.50 745.04 0.940
## envE9 399.61 745.04 0.536
##
## Correlation of Fixed Effects:
## (Intr) envE10 envE11 envE2 envE3 envE4 envE5 envE6 envE7
## envE10 -0.707
## envE11 -0.707 0.500
## envE2 -0.707 0.500 0.500
## envE3 -0.707 0.500 0.500 0.500
## envE4 -0.707 0.500 0.500 0.500 0.500
## envE5 -0.707 0.500 0.500 0.500 0.500 0.500
## envE6 -0.707 0.500 0.500 0.500 0.500 0.500 0.500
## envE7 -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## envE8 -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## envE9 -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## envE8
## envE10
## envE11
## envE2
## envE3
## envE4
## envE5
## envE6
## envE7
## envE8
## envE9 0.500
## [1]
## [1] Stability
## [1] ----------------------------------------------------
## Treatment Slope Intercept Mean SD b
## 1 1 1.4371854 -519.540201 2457.727 694.3969 0.43718540
## 2 2 0.7529629 493.528808 2053.364 359.1532 -0.24703714
## 3 3 0.8678092 383.704504 2181.455 416.4498 -0.13219080
## 4 4 0.8428426 426.425245 2172.455 384.2841 -0.15715741
## 5 5 0.8954853 -118.720032 1736.364 466.4005 -0.10451473
## 6 6 0.9302448 246.726824 2173.818 421.7411 -0.06975521
## 7 7 1.0134538 -239.466888 1860.000 496.6359 0.01345384
## 8 8 0.9013210 -9.082115 1858.091 405.0497 -0.09867896
## 9 9 0.9022891 184.003401 2053.182 514.3938 -0.09771092
## 10 10 1.3039264 -475.481353 2225.727 668.1058 0.30392638
## 11 11 1.2222482 -273.640708 2258.364 582.7875 0.22224816
## 12 12 1.6135014 -1260.977590 2081.545 883.7377 0.61350143
## 13 13 0.7168354 600.461273 2085.455 385.8571 -0.28316462
## 14 14 0.6847354 502.414077 1920.909 389.6428 -0.31526464
## 15 15 0.9749964 139.746846 2159.545 493.3809 -0.02500360
## 16 16 0.8326711 392.405551 2117.364 423.7561 -0.16732890
## 17 17 1.1997387 -562.646605 1922.727 581.8160 0.19973872
## 18 18 0.9077530 90.138965 1970.636 446.1592 -0.09224702
## Pb bR2
## 1 0.06796959 0.3232929699
## 2 0.03765971 0.3971957795
## 3 0.30632842 0.1155826760
## 4 0.05274230 0.3557873414
## 5 0.58732928 0.0339946462
## 6 0.34517872 0.0993177085
## 7 0.93534335 0.0007726187
## 8 0.10254631 0.2684395841
## 9 0.69896421 0.0174093261
## 10 0.26263331 0.1369371880
## 11 0.20902670 0.1690456689
## 12 0.15294373 0.2130733625
## 13 0.12186434 0.2447356318
## 14 0.12224680 0.2443021526
## 15 0.89303284 0.0021213177
## 16 0.31735312 0.1107330241
## 17 0.29586138 0.1203746658
## 18 0.54524179 0.0420556074
## [1]
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -646.71 -134.68 -18.94 139.41 859.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.142e+03 1.034e+02 20.727 < 2e-16 ***
## genG10 -4.044e+02 1.172e+02 -3.450 0.000708 ***
## genG11 -2.763e+02 1.172e+02 -2.357 0.019556 *
## genG12 -2.853e+02 1.172e+02 -2.434 0.015972 *
## genG13 -7.214e+02 1.172e+02 -6.155 5.28e-09 ***
## genG14 -2.839e+02 1.172e+02 -2.422 0.016475 *
## genG15 -5.977e+02 1.172e+02 -5.100 9.04e-07 ***
## genG16 -5.996e+02 1.172e+02 -5.116 8.39e-07 ***
## genG17 -4.045e+02 1.172e+02 -3.452 0.000704 ***
## genG18 -2.320e+02 1.172e+02 -1.980 0.049383 *
## genG2 -1.994e+02 1.172e+02 -1.701 0.090775 .
## genG3 -3.762e+02 1.172e+02 -3.210 0.001590 **
## genG4 -3.723e+02 1.172e+02 -3.176 0.001773 **
## genG5 -5.368e+02 1.172e+02 -4.580 8.98e-06 ***
## genG6 -2.982e+02 1.172e+02 -2.544 0.011849 *
## genG7 -3.404e+02 1.172e+02 -2.904 0.004175 **
## genG8 -5.350e+02 1.172e+02 -4.565 9.59e-06 ***
## genG9 -4.871e+02 1.172e+02 -4.156 5.14e-05 ***
## envE10 5.331e+02 9.162e+01 5.819 2.90e-08 ***
## envE11 4.291e+02 9.162e+01 4.684 5.77e-06 ***
## envE2 1.467e+01 9.162e+01 0.160 0.873009
## envE3 -9.711e+01 9.162e+01 -1.060 0.290689
## envE4 -6.310e+02 9.162e+01 -6.887 1.07e-10 ***
## envE5 8.362e+02 9.162e+01 9.127 < 2e-16 ***
## envE6 6.440e+02 9.162e+01 7.029 4.90e-11 ***
## envE7 6.394e+02 9.162e+01 6.979 6.47e-11 ***
## envE8 7.005e+02 9.162e+01 7.646 1.49e-12 ***
## envE9 3.996e+02 9.162e+01 4.362 2.24e-05 ***
## egen:eenv 5.867e-04 2.755e-04 2.130 0.034651 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 274.9 on 169 degrees of freedom
## Multiple R-squared: 0.7632, Adjusted R-squared: 0.7239
## F-statistic: 19.45 on 28 and 169 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 17 5599202 329365 4.360 2.2e-07 ***
## env 10 35202247 3520225 46.596 < 2e-16 ***
## egen:eenv 1 342634 342634 4.535 0.0347 *
## Residuals 169 12767711 75549
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1]
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -701.95 -113.36 -18.73 113.68 832.25
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.171e+03 1.164e+02 18.649 < 2e-16 ***
## genG10 -4.044e+02 1.141e+02 -3.545 0.000522 ***
## genG11 -2.763e+02 1.141e+02 -2.422 0.016611 *
## genG12 -2.853e+02 1.141e+02 -2.501 0.013447 *
## genG13 -7.214e+02 1.141e+02 -6.324 2.67e-09 ***
## genG14 -2.839e+02 1.141e+02 -2.489 0.013889 *
## genG15 -5.977e+02 1.141e+02 -5.240 5.25e-07 ***
## genG16 -5.996e+02 1.141e+02 -5.256 4.86e-07 ***
## genG17 -4.045e+02 1.141e+02 -3.546 0.000519 ***
## genG18 -2.320e+02 1.141e+02 -2.034 0.043706 *
## genG2 -1.994e+02 1.141e+02 -1.748 0.082531 .
## genG3 -3.762e+02 1.141e+02 -3.298 0.001212 **
## genG4 -3.723e+02 1.141e+02 -3.263 0.001358 **
## genG5 -5.368e+02 1.141e+02 -4.706 5.62e-06 ***
## genG6 -2.982e+02 1.141e+02 -2.614 0.009846 **
## genG7 -3.404e+02 1.141e+02 -2.984 0.003316 **
## genG8 -5.350e+02 1.141e+02 -4.690 6.01e-06 ***
## genG9 -4.871e+02 1.141e+02 -4.270 3.42e-05 ***
## envE10 4.839e+02 1.333e+02 3.630 0.000386 ***
## envE11 3.895e+02 1.197e+02 3.255 0.001394 **
## envE2 1.331e+01 8.922e+01 0.149 0.881572
## envE3 -8.815e+01 9.099e+01 -0.969 0.334144
## envE4 -5.728e+02 1.474e+02 -3.887 0.000151 ***
## envE5 7.591e+02 1.792e+02 4.235 3.93e-05 ***
## envE6 5.846e+02 1.493e+02 3.916 0.000135 ***
## envE7 5.804e+02 1.486e+02 3.906 0.000141 ***
## envE8 6.359e+02 1.578e+02 4.029 8.81e-05 ***
## envE9 3.627e+02 1.161e+02 3.125 0.002126 **
## genG1:eenv 5.294e-01 2.705e-01 1.957 0.052178 .
## genG10:eenv -1.548e-01 2.705e-01 -0.572 0.568066
## genG11:eenv -3.994e-02 2.705e-01 -0.148 0.882820
## genG12:eenv -6.491e-02 2.705e-01 -0.240 0.810710
## genG13:eenv -1.227e-02 2.705e-01 -0.045 0.963892
## genG14:eenv 2.249e-02 2.705e-01 0.083 0.933853
## genG15:eenv 1.057e-01 2.705e-01 0.391 0.696565
## genG16:eenv -6.432e-03 2.705e-01 -0.024 0.981064
## genG17:eenv -5.464e-03 2.705e-01 -0.020 0.983913
## genG18:eenv 3.962e-01 2.705e-01 1.464 0.145149
## genG2:eenv 3.145e-01 2.705e-01 1.162 0.246862
## genG3:eenv 7.057e-01 2.705e-01 2.609 0.009992 **
## genG4:eenv -1.909e-01 2.705e-01 -0.706 0.481462
## genG5:eenv -2.230e-01 2.705e-01 -0.824 0.411037
## genG6:eenv 6.724e-02 2.705e-01 0.249 0.804044
## genG7:eenv -7.508e-02 2.705e-01 -0.278 0.781755
## genG8:eenv 2.920e-01 2.705e-01 1.079 0.282175
## genG9:eenv NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 267.5 on 153 degrees of freedom
## Multiple R-squared: 0.7969, Adjusted R-squared: 0.7385
## F-statistic: 13.64 on 44 and 153 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -701.95 -113.36 -18.73 113.68 832.25
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## genG1 2457.7273 78.3908 31.352 < 2e-16 ***
## genG10 2053.3636 78.3908 26.194 < 2e-16 ***
## genG11 2181.4545 78.3908 27.828 < 2e-16 ***
## genG12 2172.4545 78.3908 27.713 < 2e-16 ***
## genG13 1736.3636 78.3908 22.150 < 2e-16 ***
## genG14 2173.8182 78.3908 27.731 < 2e-16 ***
## genG15 1860.0000 78.3908 23.727 < 2e-16 ***
## genG16 1858.0909 78.3908 23.703 < 2e-16 ***
## genG17 2053.1818 78.3908 26.192 < 2e-16 ***
## genG18 2225.7273 78.3908 28.393 < 2e-16 ***
## genG2 2258.3636 78.3908 28.809 < 2e-16 ***
## genG3 2081.5455 78.3908 26.553 < 2e-16 ***
## genG4 2085.4545 78.3908 26.603 < 2e-16 ***
## genG5 1920.9091 78.3908 24.504 < 2e-16 ***
## genG6 2159.5455 78.3908 27.548 < 2e-16 ***
## genG7 2117.3636 78.3908 27.010 < 2e-16 ***
## genG8 1922.7273 78.3908 24.527 < 2e-16 ***
## genG9 1970.6364 78.3908 25.139 < 2e-16 ***
## genG1:eenv 1.4372 0.1859 7.730 1.07e-12 ***
## genG10:eenv 0.7530 0.1859 4.050 7.92e-05 ***
## genG11:eenv 0.8678 0.1859 4.668 6.35e-06 ***
## genG12:eenv 0.8428 0.1859 4.534 1.12e-05 ***
## genG13:eenv 0.8955 0.1859 4.817 3.33e-06 ***
## genG14:eenv 0.9302 0.1859 5.004 1.45e-06 ***
## genG15:eenv 1.0135 0.1859 5.451 1.83e-07 ***
## genG16:eenv 0.9013 0.1859 4.848 2.90e-06 ***
## genG17:eenv 0.9023 0.1859 4.853 2.84e-06 ***
## genG18:eenv 1.3039 0.1859 7.014 5.98e-11 ***
## genG2:eenv 1.2222 0.1859 6.574 6.40e-10 ***
## genG3:eenv 1.6135 0.1859 8.679 4.06e-15 ***
## genG4:eenv 0.7168 0.1859 3.856 0.000166 ***
## genG5:eenv 0.6847 0.1859 3.683 0.000314 ***
## genG6:eenv 0.9750 0.1859 5.244 4.84e-07 ***
## genG7:eenv 0.8327 0.1859 4.479 1.41e-05 ***
## genG8:eenv 1.1997 0.1859 6.453 1.21e-09 ***
## genG9:eenv 0.9078 0.1859 4.883 2.49e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 260 on 162 degrees of freedom
## Multiple R-squared: 0.9879, Adjusted R-squared: 0.9852
## F-statistic: 366.8 on 36 and 162 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 18 855318146 47517675 702.96 <2e-16 ***
## gen:eenv 18 37361982 2075666 30.71 <2e-16 ***
## Residuals 162 10950610 67596
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 17 5599202 329365 4.602 9.83e-08 ***
## env 10 35202247 3520225 49.184 < 2e-16 ***
## gen:eenv 17 2159734 127043 1.775 0.0359 *
## Residuals 153 10950610 71573
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
## Estimate Std. Error t value Pr(>|t|)
## genG1:eenv 1.4371854 0.1859143 2.35154309 0.0099493339
## genG10:eenv 0.7529629 0.1859143 -1.32876913 0.0928963681
## genG11:eenv 0.8678092 0.1859143 -0.71103095 0.2390437689
## genG12:eenv 0.8428426 0.1859143 -0.84532197 0.1995889309
## genG13:eenv 0.8954853 0.1859143 -0.56216628 0.2873898747
## genG14:eenv 0.9302448 0.1859143 -0.37520093 0.3540009053
## genG15:eenv 1.0134538 0.1859143 0.07236585 0.4712000135
## genG16:eenv 0.9013210 0.1859143 -0.53077671 0.2981502055
## genG17:eenv 0.9022891 0.1859143 -0.52556978 0.2999529029
## genG18:eenv 1.3039264 0.1859143 1.63476635 0.0520198576
## genG2:eenv 1.2222482 0.1859143 1.19543360 0.1168323263
## genG3:eenv 1.6135014 0.1859143 3.29991588 0.0005946893
## genG4:eenv 0.7168354 0.1859143 -1.52309251 0.0648426184
## genG5:eenv 0.6847354 0.1859143 -1.69575281 0.0459268312
## genG6:eenv 0.9749964 0.1859143 -0.13448994 0.4465910566
## genG7:eenv 0.8326711 0.1859143 -0.90003261 0.1847194260
## genG8:eenv 1.1997387 0.1859143 1.07435929 0.1421296407
## genG9:eenv 0.9077530 0.1859143 -0.49618045 0.3102198180
## [1]
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 835.5741
## [1] Interaction sd Value:
## [1] 278.5247
## [1] Error sd Value:
## [1] NaN
## [1] Pairs:
## [[1]]
## [1] 12 3
##
## [1]
## [1]data(cornelius.maize)
mixed.res <- standard.sensitivity.plot(cornelius.maize,
response = "yield",
TreatmentName = "gen",
TrialName = "env",
dual.dendrogram=TRUE,
plot.outliers=TRUE,legend.columns=3)## Warning in anova.lm(base.lm): ANOVA F-tests on an essentially perfect fit
## are unreliable
print.stdplot(mixed.res)## [1] ----------------------------------------------------
## [1] Effects
## NULL
## NULL
## [1] Means
## [,1]
## 1 3612.667
## 2 3827.111
## 3 5605.778
## 4 4923.889
## 5 4578.222
## 6 6892.556
## 7 2992.444
## 8 6959.556
## 9 5155.556
## 10 4282.889
## 11 5323.778
## 12 6699.000
## 13 7347.333
## 14 5875.222
## 15 4953.333
## 16 4364.889
## 17 2831.889
## 18 3148.222
## 19 2223.778
## 20 5565.222
## [,1]
## 1 4617.10
## 2 4603.30
## 3 4822.85
## 4 5217.90
## 5 5247.05
## 6 5330.20
## 7 4672.40
## 8 4283.15
## 9 4929.55
## [1] Row Col Means
## [1] 3612.667 4209.444 5105.111 5230.111 4955.111 6305.444 3229.444
## [8] 4027.778 4970.667 2936.444 5307.222 7516.667 6332.333 6052.111
## [15] 5048.889 5406.000 4876.778 4551.444 2652.222 4837.444
## X1 X2 X3 X4 X5 X6 X7 X8 X9
## 4617.10 4603.30 4822.85 5217.90 5247.05 5330.20 4672.40 4283.15 4929.55
## [1] ----------------------------------------------------
## [1] AOV
## [1] ----------------------------------------------------
## Analysis of Variance Table
##
## Response: yield
## Df Sum Sq Mean Sq F value Pr(>F)
## env 19 247399973 13021051
## gen 8 19960404 2495051
## env:gen 152 62420142 410659
## Residuals 0 0
## [1] Mixed Model
## [1] ----------------------------------------------------
## Linear mixed model fit by REML ['lmerMod']
## Formula: yield ~ env + (1 | env)
## Data: plot.dat
##
## REML criterion at convergence: 2602.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.08736 -0.61738 -0.00426 0.64595 2.76388
##
## Random effects:
## Groups Name Variance Std.Dev.
## env (Intercept) 2226600 1492.2
## Residual 514878 717.6
## Number of obs: 180, groups: env, 20
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3612.7 1511.2 2.391
## envE02 596.8 2137.2 0.279
## envE03 1492.4 2137.2 0.698
## envE04 1617.4 2137.2 0.757
## envE05 1342.4 2137.2 0.628
## envE06 2692.8 2137.2 1.260
## envE07 -383.2 2137.2 -0.179
## envE08 415.1 2137.2 0.194
## envE09 1358.0 2137.2 0.635
## envE10 -676.2 2137.2 -0.316
## envE11 1694.6 2137.2 0.793
## envE12 3904.0 2137.2 1.827
## envE13 2719.7 2137.2 1.272
## envE14 2439.4 2137.2 1.141
## envE15 1436.2 2137.2 0.672
## envE16 1793.3 2137.2 0.839
## envE17 1264.1 2137.2 0.592
## envE18 938.8 2137.2 0.439
## envE19 -960.4 2137.2 -0.449
## envE20 1224.8 2137.2 0.573##
## Correlation matrix not shown by default, as p = 20 > 12.
## Use print(summary(fit$lmer), correlation=TRUE) or
## vcov(summary(fit$lmer)) if you need it## [1]
## [1] Stability
## [1] ----------------------------------------------------
## Treatment Slope Intercept Mean SD b
## 1 1 0.9814750 -151.06934 4617.10 1362.2027 -0.01852496
## 2 2 0.9649816 -84.74141 4603.30 1254.0401 -0.03501841
## 3 3 0.9540153 188.08481 4822.85 1206.9871 -0.04598473
## 4 4 1.3142584 -1166.98659 5217.90 1707.5318 0.31425845
## 5 5 1.2280664 -719.10125 5247.05 1565.8725 0.22806640
## 6 6 1.0574596 192.88517 5330.20 1348.6694 0.05745957
## 7 7 0.8575980 506.04604 4672.40 1153.8584 -0.14240201
## 8 8 0.5240001 1737.47020 4283.15 882.0533 -0.47599990
## 9 9 1.1181456 -502.58763 4929.55 1457.8590 0.11814559
## Pb bR2
## 1 0.8909193724 0.001073705
## 2 0.7110067554 0.007810197
## 3 0.5384706179 0.021380030
## 4 0.0230407710 0.255349942
## 5 0.0379595028 0.217969243
## 6 0.5214449913 0.023203364
## 7 0.1768890353 0.098897030
## 8 0.0009673339 0.462629361
## 9 0.2980285266 0.059977186
## [1]
## [1] Tukey's 1 d.f.
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1706.15 -298.66 -8.26 359.07 2113.48
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.372e+03 2.359e+02 14.293 < 2e-16 ***
## genG2 -1.380e+01 1.891e+02 -0.073 0.941930
## genG3 2.058e+02 1.891e+02 1.088 0.278384
## genG4 6.008e+02 1.891e+02 3.177 0.001807 **
## genG5 6.300e+02 1.891e+02 3.331 0.001089 **
## genG6 7.131e+02 1.891e+02 3.770 0.000233 ***
## genG7 5.530e+01 1.891e+02 0.292 0.770389
## genG8 -3.339e+02 1.891e+02 -1.766 0.079465 .
## genG9 3.124e+02 1.891e+02 1.652 0.100605
## envE02 5.968e+02 2.819e+02 2.117 0.035925 *
## envE03 1.492e+03 2.819e+02 5.294 4.16e-07 ***
## envE04 1.617e+03 2.819e+02 5.737 5.10e-08 ***
## envE05 1.342e+03 2.819e+02 4.761 4.47e-06 ***
## envE06 2.693e+03 2.819e+02 9.551 < 2e-16 ***
## envE07 -3.832e+02 2.819e+02 -1.359 0.176098
## envE08 4.151e+02 2.819e+02 1.472 0.143009
## envE09 1.358e+03 2.819e+02 4.817 3.52e-06 ***
## envE10 -6.762e+02 2.819e+02 -2.398 0.017684 *
## envE11 1.695e+03 2.819e+02 6.010 1.33e-08 ***
## envE12 3.904e+03 2.819e+02 13.847 < 2e-16 ***
## envE13 2.720e+03 2.819e+02 9.646 < 2e-16 ***
## envE14 2.439e+03 2.819e+02 8.652 6.97e-15 ***
## envE15 1.436e+03 2.819e+02 5.094 1.03e-06 ***
## envE16 1.793e+03 2.819e+02 6.361 2.27e-09 ***
## envE17 1.264e+03 2.819e+02 4.484 1.44e-05 ***
## envE18 9.388e+02 2.819e+02 3.330 0.001093 **
## envE19 -9.604e+02 2.819e+02 -3.407 0.000843 ***
## envE20 1.225e+03 2.819e+02 4.344 2.55e-05 ***
## egen:eenv 5.536e-04 1.142e-04 4.848 3.07e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 598.1 on 151 degrees of freedom
## Multiple R-squared: 0.8362, Adjusted R-squared: 0.8058
## F-statistic: 27.53 on 28 and 151 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 8 19960404 2495051 6.975 8.28e-08 ***
## env 19 247399973 13021051 36.402 < 2e-16 ***
## egen:eenv 1 8406983 8406983 23.503 3.07e-06 ***
## Residuals 151 54013159 357703
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1]
## [1] Heterogenous Slopes
## [1] ----------------------------------------------------
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1610.55 -334.46 15.47 324.12 2208.91
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.224e+03 2.697e+02 11.956 < 2e-16 ***
## genG2 -1.380e+01 1.880e+02 -0.073 0.941597
## genG3 2.058e+02 1.880e+02 1.094 0.275688
## genG4 6.008e+02 1.880e+02 3.195 0.001717 **
## genG5 6.300e+02 1.880e+02 3.350 0.001031 **
## genG6 7.131e+02 1.880e+02 3.792 0.000219 ***
## genG7 5.530e+01 1.880e+02 0.294 0.769109
## genG8 -3.339e+02 1.880e+02 -1.776 0.077844 .
## genG9 3.124e+02 1.880e+02 1.662 0.098756 .
## envE02 6.673e+02 2.875e+02 2.321 0.021681 *
## envE03 1.669e+03 3.225e+02 5.174 7.56e-07 ***
## envE04 1.809e+03 3.294e+02 5.491 1.76e-07 ***
## envE05 1.501e+03 3.149e+02 4.766 4.54e-06 ***
## envE06 3.011e+03 4.018e+02 7.493 6.26e-12 ***
## envE07 -4.285e+02 2.833e+02 -1.513 0.132571
## envE08 4.642e+02 2.838e+02 1.636 0.104126
## envE09 1.518e+03 3.157e+02 4.810 3.76e-06 ***
## envE10 -7.561e+02 2.895e+02 -2.612 0.009956 **
## envE11 1.895e+03 3.338e+02 5.677 7.30e-08 ***
## envE12 4.365e+03 5.028e+02 8.682 7.69e-15 ***
## envE13 3.041e+03 4.039e+02 7.529 5.13e-12 ***
## envE14 2.728e+03 3.829e+02 7.124 4.63e-11 ***
## envE15 1.606e+03 3.196e+02 5.024 1.47e-06 ***
## envE16 2.005e+03 3.396e+02 5.904 2.44e-08 ***
## envE17 1.413e+03 3.112e+02 4.542 1.17e-05 ***
## envE18 1.050e+03 2.977e+02 3.526 0.000567 ***
## envE19 -1.074e+03 2.985e+02 -3.597 0.000441 ***
## envE20 1.369e+03 3.094e+02 4.426 1.88e-05 ***
## genG1:eenv -1.367e-01 1.604e-01 -0.852 0.395562
## genG2:eenv -1.532e-01 1.604e-01 -0.955 0.341201
## genG3:eenv -1.641e-01 1.604e-01 -1.023 0.307869
## genG4:eenv 1.961e-01 1.604e-01 1.223 0.223428
## genG5:eenv 1.099e-01 1.604e-01 0.685 0.494232
## genG6:eenv -6.069e-02 1.604e-01 -0.378 0.705714
## genG7:eenv -2.606e-01 1.604e-01 -1.624 0.106461
## genG8:eenv -5.941e-01 1.604e-01 -3.704 0.000301 ***
## genG9:eenv NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 594.6 on 144 degrees of freedom
## Multiple R-squared: 0.8456, Adjusted R-squared: 0.8081
## F-statistic: 22.53 on 35 and 144 DF, p-value: < 2.2e-16
##
##
## Call:
## lm(formula = form, data = nonadditivity.res$multiplicative.lm$model)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1610.55 -334.46 15.47 324.12 2208.91
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## genG1 4617.1000 125.3564 36.832 < 2e-16 ***
## genG2 4603.3000 125.3564 36.722 < 2e-16 ***
## genG3 4822.8500 125.3564 38.473 < 2e-16 ***
## genG4 5217.9000 125.3564 41.625 < 2e-16 ***
## genG5 5247.0500 125.3564 41.857 < 2e-16 ***
## genG6 5330.2000 125.3564 42.520 < 2e-16 ***
## genG7 4672.4000 125.3564 37.273 < 2e-16 ***
## genG8 4283.1500 125.3564 34.168 < 2e-16 ***
## genG9 4929.5500 125.3564 39.324 < 2e-16 ***
## genG1:eenv 0.9815 0.1069 9.179 < 2e-16 ***
## genG2:eenv 0.9650 0.1069 9.025 5.03e-16 ***
## genG3:eenv 0.9540 0.1069 8.922 9.36e-16 ***
## genG4:eenv 1.3143 0.1069 12.291 < 2e-16 ***
## genG5:eenv 1.2281 0.1069 11.485 < 2e-16 ***
## genG6:eenv 1.0575 0.1069 9.890 < 2e-16 ***
## genG7:eenv 0.8576 0.1069 8.020 2.00e-13 ***
## genG8:eenv 0.5240 0.1069 4.901 2.30e-06 ***
## genG9:eenv 1.1181 0.1069 10.457 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 560.6 on 162 degrees of freedom
## Multiple R-squared: 0.9889, Adjusted R-squared: 0.9876
## F-statistic: 800.3 on 18 and 162 DF, p-value: < 2.2e-16
##
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 9 4.268e+09 474253490 1508.99 <2e-16 ***
## gen:eenv 9 2.589e+08 28767336 91.53 <2e-16 ***
## Residuals 162 5.091e+07 314285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 8 19960404 2495051 7.057 7.62e-08 ***
## env 19 247399973 13021051 36.827 < 2e-16 ***
## gen:eenv 8 11506049 1438256 4.068 0.000217 ***
## Residuals 144 50914093 353570
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ARM Table
## Estimate Std. Error t value Pr(>|t|)
## genG1:eenv 0.9814750 0.1069259 -0.1732504 4.313354e-01
## genG2:eenv 0.9649816 0.1069259 -0.3275016 3.718557e-01
## genG3:eenv 0.9540153 0.1069259 -0.4300616 3.338612e-01
## genG4:eenv 1.3142584 0.1069259 2.9390301 1.886806e-03
## genG5:eenv 1.2280664 0.1069259 2.1329387 1.721801e-02
## genG6:eenv 1.0574596 0.1069259 0.5373775 2.958721e-01
## genG7:eenv 0.8575980 0.1069259 -1.3317822 9.240126e-02
## genG8:eenv 0.5240001 0.1069259 -4.4516800 7.898417e-06
## genG9:eenv 1.1181456 0.1069259 1.1049295 1.354142e-01
## [1]
## [1] Random Outliers
## [1] ----------------------------------------------------
## [1] Critical Value:
## [1] 1928.835
## [1] Interaction sd Value:
## [1] 642.9451
## [1] Error sd Value:
## [1] NaN
## [1] Pairs:
## [[1]]
## [1] 1 8
##
## [1]
## [1]tdf.tbl <- anova(mixed.res$tdf$multiplicative.lm)
anova(mixed.res$tdf$multiplicative.lm)## Analysis of Variance Table
##
## Response: yield
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 8 19960404 2495051 6.9752 8.283e-08 ***
## env 19 247399973 13021051 36.4018 < 2.2e-16 ***
## egen:eenv 1 8406983 8406983 23.5027 3.070e-06 ***
## Residuals 151 54013159 357703
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mixed.res$tdf$multiplicative.lm)##
## Call:
## lm(formula = as.formula(modelString), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1706.15 -298.66 -8.26 359.07 2113.48
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.372e+03 2.359e+02 14.293 < 2e-16 ***
## genG2 -1.380e+01 1.891e+02 -0.073 0.941930
## genG3 2.058e+02 1.891e+02 1.088 0.278384
## genG4 6.008e+02 1.891e+02 3.177 0.001807 **
## genG5 6.300e+02 1.891e+02 3.331 0.001089 **
## genG6 7.131e+02 1.891e+02 3.770 0.000233 ***
## genG7 5.530e+01 1.891e+02 0.292 0.770389
## genG8 -3.339e+02 1.891e+02 -1.766 0.079465 .
## genG9 3.124e+02 1.891e+02 1.652 0.100605
## envE02 5.968e+02 2.819e+02 2.117 0.035925 *
## envE03 1.492e+03 2.819e+02 5.294 4.16e-07 ***
## envE04 1.617e+03 2.819e+02 5.737 5.10e-08 ***
## envE05 1.342e+03 2.819e+02 4.761 4.47e-06 ***
## envE06 2.693e+03 2.819e+02 9.551 < 2e-16 ***
## envE07 -3.832e+02 2.819e+02 -1.359 0.176098
## envE08 4.151e+02 2.819e+02 1.472 0.143009
## envE09 1.358e+03 2.819e+02 4.817 3.52e-06 ***
## envE10 -6.762e+02 2.819e+02 -2.398 0.017684 *
## envE11 1.695e+03 2.819e+02 6.010 1.33e-08 ***
## envE12 3.904e+03 2.819e+02 13.847 < 2e-16 ***
## envE13 2.720e+03 2.819e+02 9.646 < 2e-16 ***
## envE14 2.439e+03 2.819e+02 8.652 6.97e-15 ***
## envE15 1.436e+03 2.819e+02 5.094 1.03e-06 ***
## envE16 1.793e+03 2.819e+02 6.361 2.27e-09 ***
## envE17 1.264e+03 2.819e+02 4.484 1.44e-05 ***
## envE18 9.388e+02 2.819e+02 3.330 0.001093 **
## envE19 -9.604e+02 2.819e+02 -3.407 0.000843 ***
## envE20 1.225e+03 2.819e+02 4.344 2.55e-05 ***
## egen:eenv 5.536e-04 1.142e-04 4.848 3.07e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 598.1 on 151 degrees of freedom
## Multiple R-squared: 0.8362, Adjusted R-squared: 0.8058
## F-statistic: 27.53 on 28 and 151 DF, p-value: < 2.2e-16Working backwards, standard error for genotype estimates, the heterogeneous null model, is 560.6/sqrt(20), but I still haven’t worked out the SE for heterogeneous slopes. Still, if we assume balanced, then we can use the given standard error
sqrt(357703)/sqrt(8406983)
ee <- mixed.res\(tdf\)multiplicative.lm\(model\)egenmixed.res\(tdf\)multiplicative.lm\(model\)eenv > sum(eeee) [1] 2.743446e+13 > sqrt(357703/2.743446e+13) [1] 0.0001141861
SE = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]